{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:35:30Z","timestamp":1776796530294,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"283","license":[{"start":{"date-parts":[[2014,1,28]],"date-time":"2014-01-28T00:00:00Z","timestamp":1390867200000},"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                    We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"r Superscript normal t normal h\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"normal\">t<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">h<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">r^{\\mathrm {th}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    Feng-Rao number is obtained.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2013-02673-7","type":"journal-article","created":{"date-parts":[[2013,1,28]],"date-time":"2013-01-28T13:07:22Z","timestamp":1359378442000},"page":"1813-1836","source":"Crossref","is-referenced-by-count":8,"title":["On the generalized Feng-Rao numbers of numerical semigroups generated by intervals"],"prefix":"10.1090","volume":"82","author":[{"given":"M.","family":"Delgado","sequence":"first","affiliation":[]},{"given":"J.","family":"Farr\u00e1n","sequence":"additional","affiliation":[]},{"given":"P.","family":"Garc\u00eda-S\u00e1nchez","sequence":"additional","affiliation":[]},{"given":"D.","family":"Llena","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2013,1,28]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1137\/S089548019834342X","article-title":"The weight hierarchy of Hermitian codes","volume":"13","author":"Barbero, Angela I.","year":"2000","journal-title":"SIAM J. Discrete Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0895-4801","issn-type":"print"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1006\/ffta.1999.0266","article-title":"Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models","volume":"6","author":"Campillo, A.","year":"2000","journal-title":"Finite Fields Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1071-5797","issn-type":"print"},{"issue":"7","key":"3","doi-asserted-by":"publisher","first-page":"2634","DOI":"10.1109\/18.887872","article-title":"On the parameters of algebraic-geometry codes related to Arf semigroups","volume":"46","author":"Campillo, Antonio","year":"2000","journal-title":"IEEE Trans. Inform. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0018-9448","issn-type":"print"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1515\/FORUM.2009.006","article-title":"The catenary and tame degree of numerical monoids","volume":"21","author":"Chapman, S. T.","year":"2009","journal-title":"Forum Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0933-7741","issn-type":"print"},{"key":"5","unstructured":"M. Delgado, P. A. Garc\u00eda-S\u00e1nchez and J. Morais, \u201cNumericalSgps\u201d, A GAP package for numerical semigroups, current version number 0.97 (2011). Available via http:\/\/www.gap-system.org\/."},{"key":"6","unstructured":"J. I. Farr\u00e1n, P. A. Garc\u00eda-S\u00e1nchez and D. Llena, \u201cOn the Feng-Rao numbers\u201d, Actas de las VII Jornadas de Matem\u00e1tica Discreta y Algor\u00edtmica, pp. 321-333 (2010)."},{"issue":"1","key":"7","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/S0166-218X(02)00441-9","article-title":"Goppa-like bounds for the generalized Feng-Rao distances","volume":"128","author":"Farr\u00e1n, J. I.","year":"2003","journal-title":"Discrete Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0166-218X","issn-type":"print"},{"issue":"1","key":"8","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1109\/18.179340","article-title":"Decoding algebraic-geometric codes up to the designed minimum distance","volume":"39","author":"Feng, Gui Liang","year":"1993","journal-title":"IEEE Trans. Inform. 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Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0018-9448","issn-type":"print"},{"issue":"2","key":"10","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0012-365X(77)90078-4","article-title":"The weight distribution of irreducible cyclic codes with block length \ud835\udc5b\u2081((\ud835\udc5e^{\ud835\udc59}-1)\/\ud835\udc41)","volume":"18","author":"Helleseth, Tor","year":"1977","journal-title":"Discrete Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-365X","issn-type":"print"},{"key":"11","isbn-type":"print","first-page":"871","article-title":"Algebraic geometry codes","author":"H\u00f8holdt, Tom","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/044450088X"},{"issue":"6","key":"12","doi-asserted-by":"publisher","first-page":"1720","DOI":"10.1109\/18.476245","article-title":"The minimum distance of codes in an array coming from telescopic semigroups","volume":"41","author":"Kirfel, Christoph","year":"1995","journal-title":"IEEE Trans. Inform. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0018-9448","issn-type":"print"},{"key":"13","doi-asserted-by":"crossref","unstructured":"J. C. Rosales and P. A. Garc\u00eda-S\u00e1nchez, \u201cNumerical Semigroups\u201d, Developments in Maths. vol. 20, Springer (2010).","DOI":"10.1007\/978-1-4419-0160-6"},{"issue":"5","key":"14","doi-asserted-by":"publisher","first-page":"1412","DOI":"10.1109\/18.133259","article-title":"Generalized Hamming weights for linear codes","volume":"37","author":"Wei, Victor K.","year":"1991","journal-title":"IEEE Trans. Inform. 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