{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:35:07Z","timestamp":1776832507180,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"255","license":[{"start":{"date-parts":[[2007,5,1]],"date-time":"2007-05-01T00:00:00Z","timestamp":1177977600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Let\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N Superscript asterisk Baseline left-parenthesis m right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2217\n                                  \n                                <\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N^{*}(m)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    be the minimal length of a polynomial with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"plus-or-minus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo>\n                              \u00b1\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\pm 1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    coefficients divisible by\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis x minus 1 right-parenthesis Superscript m\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:msup>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <mml:mi>m<\/mml:mi>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(x-1)^m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Byrnes noted that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N Superscript asterisk Baseline left-parenthesis m right-parenthesis less-than-or-equal-to 2 Superscript m\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2217\n                                  \n                                <\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mi>m<\/mml:mi>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N^{*}(m)\\leq 2^m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for each\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m\">\n                        <mml:semantics>\n                          <mml:mi>m<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and asked whether in fact\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N Superscript asterisk Baseline left-parenthesis m right-parenthesis equals 2 Superscript m\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2217\n                                  \n                                <\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mi>m<\/mml:mi>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N^{*}(m)=2^m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Boyd showed that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N Superscript asterisk Baseline left-parenthesis m right-parenthesis equals 2 Superscript m\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2217\n                                  \n                                <\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>m<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N^{*}(m) = 2^{m}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for all\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m less-than-or-equal-to 5\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">m \\le 5<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , but\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N Superscript asterisk Baseline left-parenthesis 6 right-parenthesis equals 48\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2217\n                                  \n                                <\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>6<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>48<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N^{*}(6) = 48<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . He further showed that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N Superscript asterisk Baseline left-parenthesis 7 right-parenthesis equals 96\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mo>\n                                \u2217\n                                \n                              <\/mml:mo>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>7<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>96<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N^*(7)=96<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N Superscript asterisk Baseline left-parenthesis 8 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2217\n                                  \n                                <\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>8<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N^{*}(8)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is one of the 5 numbers\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"96 comma 144 comma 160 comma 176\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>96<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>144<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>160<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>176<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">96, 144, 160, 176<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , or\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"192\">\n                        <mml:semantics>\n                          <mml:mn>192<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">192<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Here we prove that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N Superscript asterisk Baseline left-parenthesis 8 right-parenthesis equals 144\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>N<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\n                                  \u2217\n                                  \n                                <\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>8<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>144<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N^{*}(8) = 144<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Similarly, let\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m Superscript asterisk Baseline left-parenthesis upper N right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>m<\/mml:mi>\n                              <mml:mo>\n                                \u2217\n                                \n                              <\/mml:mo>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">m^*(N)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    be the maximal power of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis x minus 1 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(x-1)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    dividing some polynomial of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N minus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N-1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"plus-or-minus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo>\n                              \u00b1\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\pm 1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    coefficients. Boyd was able to find\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m Superscript asterisk Baseline left-parenthesis upper N right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>m<\/mml:mi>\n                              <mml:mo>\n                                \u2217\n                                \n                              <\/mml:mo>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">m^*(N)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N greater-than 88\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>88<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N&gt;88<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . In this paper we determine\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m Superscript asterisk Baseline left-parenthesis upper N right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>m<\/mml:mi>\n                              <mml:mo>\n                                \u2217\n                                \n                              <\/mml:mo>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">m^*(N)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N greater-than 168\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>168<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N&gt;168<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-06-01848-5","type":"journal-article","created":{"date-parts":[[2006,5,24]],"date-time":"2006-05-24T14:43:01Z","timestamp":1148481781000},"page":"1541-1552","source":"Crossref","is-referenced-by-count":4,"title":["Littlewood polynomials with high order zeros"],"prefix":"10.1090","volume":"75","author":[{"given":"Daniel","family":"Berend","sequence":"first","affiliation":[]},{"given":"Shahar","family":"Golan","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2006,5,1]]},"reference":[{"key":"1","isbn-type":"print","first-page":"1","article-title":"The ubiquitous Prouhet-Thue-Morse sequence","author":"Allouche, Jean-Paul","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/1852331968"},{"issue":"220","key":"2","doi-asserted-by":"publisher","first-page":"1697","DOI":"10.1090\/S0025-5718-97-00892-2","article-title":"On a problem of Byrnes concerning polynomials with restricted coefficients","volume":"66","author":"Boyd, David W.","year":"1997","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"239","key":"3","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1090\/S0025-5718-01-01360-6","article-title":"On a problem of Byrnes concerning polynomials with restricted coefficients. II","volume":"71","author":"Boyd, David W.","year":"2002","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"4","series-title":"NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-0665-5","volume-title":"Recent advances in Fourier analysis and its applications","volume":"315","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/0792308751"},{"key":"5","doi-asserted-by":"crossref","unstructured":"J.S. Byrnes and D.J. Newman, Null steering employing polynomials with restricted coefficients, IEEE Trans. Antennas and Propagation 36 (1988), 301\u2013303.","DOI":"10.1109\/8.1108"},{"key":"6","unstructured":"S. Golan, http:\/\/www.cs.bgu.ac.il\/\u223cgolansha\/polynomials."},{"key":"7","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","volume-title":"Finite fields","volume":"20","author":"Lidl, Rudolf","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/0201135191"},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"846","DOI":"10.1109\/18.661533","article-title":"Efficient encoding algorithm for third-order spectral-null codes","volume":"44","author":"Skachek, Vitaly","year":"1998","journal-title":"IEEE Trans. Inform. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0018-9448","issn-type":"print"},{"key":"9","series-title":"Computer Science and Applied Mathematics","isbn-type":"print","volume-title":"Combinatorial algorithms","author":"Nijenhuis, Albert","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0125192606","edition":"2"},{"key":"10","doi-asserted-by":"crossref","unstructured":"R.M. Roth, P.H. Siegel, and A. Vardy, High-order spectral-null codes: Constructions and bounds, IEEE Trans. Inform. Theory 35 (1989), 463\u2013472.","DOI":"10.1109\/18.32143"},{"issue":"2","key":"11","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF00124592","article-title":"Spectral-null codes and null spaces of Hadamard submatrices","volume":"9","author":"Roth, Ron M.","year":"1996","journal-title":"Des. Codes Cryptogr.","ISSN":"https:\/\/id.crossref.org\/issn\/0925-1022","issn-type":"print"},{"key":"12","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0133-2","volume-title":"Introduction to cyclotomic fields","volume":"83","author":"Washington, Lawrence C.","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/0387906223"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2006-75-255\/S0025-5718-06-01848-5\/S0025-5718-06-01848-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2006-75-255\/S0025-5718-06-01848-5\/S0025-5718-06-01848-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:37:04Z","timestamp":1776782224000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2006-75-255\/S0025-5718-06-01848-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,5,1]]},"references-count":12,"journal-issue":{"issue":"255","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["S0025-5718-06-01848-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-06-01848-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2006,5,1]]}}}