{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:02:02Z","timestamp":1772283722138,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2007,8,25]],"date-time":"2007-08-25T00:00:00Z","timestamp":1188000000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2007,9,21]]},"DOI":"10.1007\/s10623-007-9117-y","type":"journal-article","created":{"date-parts":[[2007,8,24]],"date-time":"2007-08-24T15:27:57Z","timestamp":1187969277000},"page":"247-258","source":"Crossref","is-referenced-by-count":20,"title":["Construction of MDS self-dual codes over Galois rings"],"prefix":"10.1007","volume":"45","author":[{"given":"Jon-Lark","family":"Kim","sequence":"first","affiliation":[]},{"given":"Yoonjin","family":"Lee","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,8,25]]},"reference":[{"issue":"4","key":"9117_CR1","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1109\/18.761269","volume":"45","author":"E Bannai","year":"1999","unstructured":"Bannai E, Dougherty ST, Harada M and Oura M (1999). Type II codes, even unimodular lattices and invariant rings. IEEE Trans Inform Theory 45(4): 1194\u20131205","journal-title":"IEEE Trans Inform Theory"},{"key":"9117_CR2","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/S0019-9958(72)90223-9","volume":"20","author":"IF Blake","year":"1972","unstructured":"Blake IF (1972). Codes over certain rings. Inform Contr 20: 396\u2013404","journal-title":"Inform Contr"},{"key":"9117_CR3","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/S0019-9958(75)80001-5","volume":"29","author":"IF Blake","year":"1975","unstructured":"Blake IF (1975). Codes over integer residue rings. Inform Contr 29: 295\u2013300","journal-title":"Inform Contr"},{"issue":"3","key":"9117_CR4","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1109\/18.568705","volume":"43","author":"A Bonnecaze","year":"1997","unstructured":"Bonnecaze A, Sol\u00e9 P, Bachoc C and Mourrain B (1997). Type II codes over Z 4. IEEE Trans Inform Theory 43(3): 969\u2013976","journal-title":"IEEE Trans Inform Theory"},{"issue":"4","key":"9117_CR5","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/18.86979","volume":"37","author":"RA Brualdi","year":"1991","unstructured":"Brualdi RA and Pless VS (1991). Weight enumerators of self-dual codes. IEEE Trans Inform Theory 37(4): 1222\u20131225","journal-title":"IEEE Trans Inform Theory"},{"issue":"1","key":"9117_CR6","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF01390768","volume":"6","author":"AR Calderbank","year":"1995","unstructured":"Calderbank AR and Sloane NJA (1995). Modular and p-adic cyclic codes. Des Codes Cryptogr 6(1): 21\u201335","journal-title":"Des Codes Cryptogr"},{"key":"9117_CR7","volume-title":"An Introduction to Magma","author":"J Cannon","year":"1994","unstructured":"Cannon J and Playoust C (1994). An Introduction to Magma. University of Sydney, Sydney, Australia"},{"issue":"1","key":"9117_CR8","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/0097-3165(93)90070-O","volume":"62","author":"JH Conway","year":"1993","unstructured":"Conway JH and Sloane NJA (1993). Self-dual codes over the integers modulo 4. J Combin Theory Ser A 62(1): 30\u201345","journal-title":"J Combin Theory Ser A"},{"issue":"3","key":"9117_CR9","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1109\/18.382022","volume":"41","author":"ST Dougherty","year":"1995","unstructured":"Dougherty ST (1995). Shadow codes and weight enumerators. IEEE Trans Inform Theory 41(3): 762\u2013768","journal-title":"IEEE Trans Inform Theory"},{"issue":"3","key":"9117_CR10","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1023\/A:1018696102510","volume":"9","author":"ST Dougherty","year":"1999","unstructured":"Dougherty ST, Gulliver TA and Harada M (1999). Type II self-dual codes over finite rings and even unimodular lattices. J Algebraic Combin 9(3): 233\u2013250","journal-title":"J Algebraic Combin"},{"key":"9117_CR11","unstructured":"Dougherty ST, Gulliver TA, Park YH, Wong JNC Optimal linear codes over $${\\mathbb{Z}}_m$$ . J Korean Math Soc to appear"},{"key":"9117_CR12","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s10623-006-9000-2","volume":"41","author":"ST Dougherty","year":"2006","unstructured":"Dougherty ST, Gulliver TA and Wang J (2006). Self-dual codes over Z 8 and Z 9. Des Codes Cryptogr 41: 235\u2013249","journal-title":"Des Codes Cryptogr"},{"key":"9117_CR13","doi-asserted-by":"crossref","first-page":"253","DOI":"10.14492\/hokmj\/1351001213","volume":"28","author":"ST Dougherty","year":"1999","unstructured":"Dougherty ST, Harada M and Sol\u00e9 P (1999). Self-dual codes over rings and the Chinese remainder theorem. Hokkaido Math J 28: 253\u2013283","journal-title":"Hokkaido Math J"},{"key":"9117_CR14","unstructured":"Dougherty ST, Kim J-L, Kulosman H MDS codes over finite principal ideal rings. Preprint"},{"issue":"1","key":"9117_CR15","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1109\/18.817524","volume":"46","author":"ST Dougherty","year":"2006","unstructured":"Dougherty ST and Shiromoto K (2006). MDR Codes over $${\\mathbb{Z}}_k$$ IEEE Trans Inform Theory 46(1): 265\u2013269","journal-title":"IEEE Trans Inform Theory"},{"issue":"2","key":"9117_CR16","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1142\/S1793042106000577","volume":"2","author":"P Gaborit","year":"2006","unstructured":"Gaborit P, Natividad AM and Sol\u00e9 P (2006). Eisenstein lattices, Galois rings and quaternary codes. Int J Number Theory 2(2): 289\u2013303","journal-title":"Int J Number Theory"},{"key":"9117_CR17","unstructured":"Gulliver TA, Kim J-L, Lee Y New MDS and near-MDS self-dual codes. Preprint"},{"issue":"2","key":"9117_CR18","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/18.312154","volume":"40","author":"AR Hammons","year":"1994","unstructured":"Hammons AR, Kumar PV, Calderbank AR, Sloane NJA and Sol\u00e9 P (1994). The $${\\mathbb{Z}}_4$$ -linearity of Kerdock, Preparata, Goethals, and related codesIEEE Trans Inform Theory 40(2): 301\u2013319","journal-title":"IEEE Trans Inform Theory"},{"key":"9117_CR19","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1109\/18.923739","volume":"47","author":"J-L Kim","year":"2001","unstructured":"Kim J-L (2001). New self-dual codes over GF(4) with the highest known minimum weights. IEEE Trans Inform Theory 47: 1575\u20131580","journal-title":"IEEE Trans Inform Theory"},{"key":"9117_CR20","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.jcta.2003.10.003","volume":"105","author":"J-L Kim","year":"2004","unstructured":"Kim J-L and Lee Y (2004). Euclidean and hermitian self-dual MDS codes over large finite fields. J Combin Theory Ser A 105: 79\u201395","journal-title":"J Combin Theory Ser A"},{"key":"9117_CR21","unstructured":"Lee H, Lee Y Construction of self-dual codes over finite rings $$\\mathbb {Z}_{p^m}$$ . J Combin Theory Ser A to appear"},{"key":"9117_CR22","volume-title":"Finite rings with identity. Pure Appl Math, vol. 28","author":"BR McDonald","year":"1974","unstructured":"McDonald BR (1974). Finite rings with identity. Pure Appl Math, vol. 28. Marcel Dekker, Inc., New York"},{"key":"9117_CR23","unstructured":"MacWilliams FJ, Sloane NJA (1977) The theory of error-correcting codes. Amsterdam, The Netherlands North-Holland"},{"key":"9117_CR24","unstructured":"Nebe G, Rains EM, Sloane NJA (2006) Self-dual codes and invariant theory. Springer, Berlin, February (2006)"},{"issue":"6","key":"9117_CR25","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/PL00012382","volume":"10","author":"GH Norton","year":"2000","unstructured":"Norton GH and Salagean A (2000). On the structure of linear and cyclic codes over a finite chain ring. Appl Algebra Eng Commun Comput 10(6): 489\u2013506","journal-title":"Appl Algebra Eng Commun Comput"},{"issue":"3","key":"9117_CR26","doi-asserted-by":"crossref","first-page":"1060","DOI":"10.1109\/18.841186","volume":"46","author":"GH Norton","year":"2000","unstructured":"Norton GH and Salagean A (2000). On the Hamming distance of linear codes over a finite chain ring. IEEE Trans Inform Theory 46(3): 1060\u20131067","journal-title":"IEEE Trans Inform Theory"},{"issue":"1","key":"9117_CR27","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1006\/ffta.1996.0172","volume":"3","author":"V Pless","year":"1997","unstructured":"Pless V, Sol\u00e9 P and Qian Z (1997). Cyclic self-dual $${\\mathbb{Z}}_4$$ -codesFinite Fields Appl 3(1): 48\u201369","journal-title":"Finite Fields Appl"},{"key":"9117_CR28","unstructured":"Rains E, Sloane NJA (1998) Self-dual codes. In: Pless VS, Huffman WC (Eds) Handbook of coding theory. Elsevier, Amsterdam. The Netherlands"},{"key":"9117_CR29","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1109\/TIT.1979.1056063","volume":"25","author":"P Shankar","year":"1979","unstructured":"Shankar P (1979). On BCH codes over arbitrary integer rings. IEEE Trans Inform Theory 25: 480\u2013483","journal-title":"IEEE Trans Inform Theory"},{"key":"9117_CR30","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/S0019-9958(77)90526-5","volume":"35","author":"E Spiegel","year":"1997","unstructured":"Spiegel E (1997). Codes over Z m . Inform Contr 35: 48\u201352","journal-title":"Inform Contr"},{"key":"9117_CR31","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/S0019-9958(78)90461-8","volume":"37","author":"E Spiegel","year":"1978","unstructured":"Spiegel E (1978). Codes over Z m revisited. Inform Contr 37: 100\u2013104","journal-title":"Inform Contr"},{"key":"9117_CR32","doi-asserted-by":"crossref","DOI":"10.1142\/5350","volume-title":"Lectures on finite fields and Galois rings","author":"Z-X Wan","year":"2003","unstructured":"Wan Z-X (2003). Lectures on finite fields and Galois rings. World Scientific Publishing Co. Inc., River Edge, NJ"},{"issue":"3","key":"9117_CR33","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1353\/ajm.1999.0024","volume":"121","author":"JA Wood","year":"1999","unstructured":"Wood JA (1999). Duality for modules over finite rings and applications to coding theory. Am J Math 121(3): 555\u2013575","journal-title":"Am J Math"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-007-9117-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-007-9117-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-007-9117-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T19:50:08Z","timestamp":1559245808000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-007-9117-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,8,25]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,9,21]]}},"alternative-id":["9117"],"URL":"https:\/\/doi.org\/10.1007\/s10623-007-9117-y","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,8,25]]}}}