{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T03:36:25Z","timestamp":1775014585073,"version":"3.50.1"},"reference-count":34,"publisher":"Pleiades Publishing Ltd","issue":"3","license":[{"start":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T00:00:00Z","timestamp":1435708800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T00:00:00Z","timestamp":1435708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Probl Inf Transm"],"published-print":{"date-parts":[[2015,7]]},"DOI":"10.1134\/s0032946015030023","type":"journal-article","created":{"date-parts":[[2015,10,18]],"date-time":"2015-10-18T19:14:15Z","timestamp":1445195655000},"page":"217-230","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Decoding of repeated-root cyclic codes up to new bounds on their minimum distance"],"prefix":"10.1134","volume":"51","author":[{"given":"A.","family":"Zeh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Ulmschneider","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2015,10,18]]},"reference":[{"issue":"1","key":"4239_CR1","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/S0019-9958(60)90287-4","volume":"3","author":"R.C. Bose","year":"1960","unstructured":"Bose, R.C. and Ray-Chaudhuri, D.K. On a Class of Error Correcting Binary Group Codes, Inform. Control, 1960, vol. 3, no. 1, pp. 68\u201379.","journal-title":"Inform. Control"},{"key":"4239_CR2","first-page":"147","volume":"2","author":"A. Hocquenghem","year":"1959","unstructured":"Hocquenghem, A. Codes correcteurs d\u2019erreurs, Chiffres, 1959, vol. 2, pp. 147\u2013156.","journal-title":"Chiffres"},{"issue":"3","key":"4239_CR3","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1109\/TIT.1972.1054824","volume":"18","author":"C.R.P. Hartmann","year":"1972","unstructured":"Hartmann, C.R.P. Decoding beyond the BCH Bound, IEEE Trans. Inform. Theory, 1972, vol. 18, no. 3, pp. 441\u2013444.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"5","key":"4239_CR4","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1016\/S0019-9958(72)90887-X","volume":"20","author":"C.R.P. Hartmann","year":"1972","unstructured":"Hartmann, C.R.P. and Tzeng, K.K. Generalizations of the BCH Bound, Inform. Control, 1972, vol. 20, no. 5, pp. 489\u2013498.","journal-title":"Inform. Control"},{"issue":"3","key":"4239_CR5","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/BF01119999","volume":"3","author":"S.D. Berman","year":"1967","unstructured":"Berman, S.D. Semisimple Cyclic and Abelian Codes, Cybernetics, 1967, vol. 3, no. 3, pp. 17\u201323.","journal-title":"Cybernetics"},{"issue":"1","key":"4239_CR6","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1109\/TIT.1973.1054936","volume":"19","author":"J.L. Massey","year":"1973","unstructured":"Massey, J.L. Costello, D.J., and Justesen, J., PolynomialWeights and Code Constructions, IEEE Trans. Inform. Theory, 1973, vol. 19, no. 1, pp. 101\u2013110.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"4239_CR7","first-page":"39","volume-title":"Proc. 1986 IEEE Int. Sympos. on Information Theory (ISIT\u20191986), Ann Arbor, MI,USA, Oct. 6\u20139","author":"J.L. Massey","year":"1986","unstructured":"Massey, J.L. von Seemann, N., and Sch\u00f6ller, P., Hasse Derivatives and Repeated-Root Cyclic Codes, in Proc. 1986 IEEE Int. Sympos. on Information Theory (ISIT\u20191986), Ann Arbor, MI,USA, Oct. 6\u20139, 1986, p. 39."},{"key":"4239_CR8","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/978-1-4615-2694-0_10","volume-title":"Communications and Cryptography: Two Sides of One Tapestry","author":"V.C. da Rocha","year":"1994","unstructured":"da Rocha, V.C. On Repeated-Single-Root Constacyclic Codes, Communications and Cryptography: Two Sides of One Tapestry, Blahut, R.E., Costello, D.J., Jr., Maurer U., and Mittelholzer, T., Eds., Boston: Kluwer, 1994, pp. 93\u201399."},{"key":"4239_CR9","volume-title":"On the Minimum Distance of Long Cyclic Codes and Cyclic Redundancy Check Codes","author":"G. Castagnoli","year":"1989","unstructured":"Castagnoli, G. On the Minimum Distance of Long Cyclic Codes and Cyclic Redundancy Check Codes, PhD Thesis, Z\u00fcrich, Switzerland: ETH, 1989."},{"key":"4239_CR10","first-page":"164","volume":"357","author":"G. Castagnoli","year":"1989","unstructured":"Castagnoli, G. On the Asymptotic Badness of Cyclic Codes with Block-Lengths Composed from a Fixed Set of Prime Factors, Proc. 6th Int. Conf. on Applied Algebra, Algebraic Algorithms and Error- Correcting Codes (AAECC-6), Rome, Italy, July 4\u20138, 1988. Mora, T. Ed., Lect. Notes Comput. Sci., vol. 357, Berlin: Springer, 1989, pp. 164\u2013168.","journal-title":"Proc. 6th Int. Conf. on Applied Algebra, Algebraic Algorithms and Error- Correcting Codes (AAECC-6), Rome, Italy, July 4\u20138, 1988"},{"issue":"2","key":"4239_CR11","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1109\/18.75249","volume":"37","author":"G. Castagnoli","year":"1991","unstructured":"Castagnoli, G. Massey, J.L., Sch\u00f6ller, P.A., and von Seemann, N., On Repeated-Root Cyclic Codes, IEEE Trans. Inform. Theory, 1991, vol. 37, no. 2, pp. 337\u2013342.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"4239_CR12","first-page":"111","volume":"7","author":"R.Kh. Latypov","year":"1979","unstructured":"Latypov, R.Kh. Checking Matrix of a Cyclic Code Generated by Multiple Roots, Issled. Prikl. Mat., 1979, no. 7, pp. 111\u2013116 [J. Soviet Math. (Engl. Transl.), 1988, vol. 43, no. 3, pp. 2492\u20132495].","journal-title":"Issled. Prikl. Mat."},{"issue":"2","key":"4239_CR13","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1109\/18.75250","volume":"37","author":"J. van Lint","year":"1991","unstructured":"van Lint, J. Repeated-Root Cyclic Codes, IEEE Trans. Inform. Theory, 1991, vol. 37, no. 2, pp. 343\u2013345.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"2","key":"4239_CR14","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1109\/18.485736","volume":"42","author":"K.-H. Zimmermann","year":"1996","unstructured":"Zimmermann, K.-H. On Generalizations of Repeated-Root Cyclic Codes, IEEE Trans. Inform. Theory, 1996, vol. 42, no. 2, pp. 641\u2013649.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"6","key":"4239_CR15","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1109\/TIT.2003.811921","volume":"49","author":"C.-S. Nedeloaia","year":"2003","unstructured":"Nedeloaia, C.-S. Weight Distributions of Cyclic Self-Dual Codes, IEEE Trans. Inform. Theory, 2003, vol. 49, no. 6, pp. 1582\u20131591.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"3","key":"4239_CR16","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/s10623-005-1431-7","volume":"38","author":"S. Ling","year":"2006","unstructured":"Ling, S. Niederreiter, H., and Sol\u00e9, P., On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots, Des. Codes Cryptogr., 2006, vol. 38, no. 3, pp. 337\u2013361.","journal-title":"Des. Codes Cryptogr."},{"issue":"1","key":"4239_CR17","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/j.ffa.2011.07.003","volume":"18","author":"H.Q. Dinh","year":"2012","unstructured":"Dinh, H.Q. Repeated-Root Constacyclic Codes of Length 2ps, Finite Fields Appl., 2012, vol. 18, no. 1, pp. 133\u2013143.","journal-title":"Finite Fields Appl."},{"issue":"9","key":"4239_CR18","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1016\/j.disc.2013.01.024","volume":"313","author":"H.Q. Dinh","year":"2013","unstructured":"Dinh, H.Q. Structure of Repeated-Root Constacyclic Codes of Length 3ps and Their Duals, Discrete Math., 2013, vol. 313, no. 9, pp. 983\u2013991.","journal-title":"Discrete Math."},{"issue":"2","key":"4239_CR19","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s10623-012-9721-3","volume":"71","author":"A. Zeh","year":"2014","unstructured":"Zeh, A. and Bezzateev, S.V. A New Bound on the Minimum Distance of Cyclic Codes Using Small- Minimum-Distance Cyclic Codes, Des. Codes Cryptogr., 2014, vol. 71, no. 2, pp. 229\u2013246.","journal-title":"Des. Codes Cryptogr."},{"issue":"6","key":"4239_CR20","doi-asserted-by":"publisher","first-page":"3951","DOI":"10.1109\/TIT.2012.2185924","volume":"58","author":"A. Zeh","year":"2012","unstructured":"Zeh, A. Wachter-Zeh, A., and Bezzateev, S.V., Decoding Cyclic Codes up to a New Bound on the Minimum Distance, IEEE Trans. Inform. Theory, 2012, vol. 58, no. 6, pp. 3951\u20133960.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"3","key":"4239_CR21","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1109\/TIT.1965.1053802","volume":"11","author":"H. Burton","year":"1965","unstructured":"Burton, H. and Weldon, E.J. Cyclic Product Codes, IEEE Trans. Inform. Theory, 1965, vol. 11, no. 3, pp. 433\u2013439.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"4","key":"4239_CR22","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1109\/TIT.1970.1054491","volume":"16","author":"S. Lin","year":"1970","unstructured":"Lin, S. and Weldon, E.J. Further Results on Cyclic Product Codes, IEEE Trans. Inform. Theory, 1970, vol. 16, no. 4, pp. 452\u2013459.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"3","key":"4239_CR23","doi-asserted-by":"publisher","first-page":"584","DOI":"10.1109\/18.30981","volume":"35","author":"G.-L. Feng","year":"1989","unstructured":"Feng, G.-L. and Tzeng, K.K. A Generalized Euclidean Algorithm for Multisequence Shift-Register Synthesis, IEEE Trans. Inform. Theory, 1989, vol. 35, no. 3, pp. 584\u2013594.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"4239_CR24","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1515\/crll.1936.175.50","volume":"175","author":"H. Hasse","year":"1936","unstructured":"Hasse, H., Theorie der h\u00f6heren Differentiale in einem algebraischen Funktionenk\u00f6rper mit vollkommenem Konstantenk\u00f6rper bei beliebiger Charakteristik, J. Reine Angew. Math., 1936, vol. 175, pp. 50\u201354.","journal-title":"J. Reine Angew. Math."},{"issue":"5","key":"4239_CR25","doi-asserted-by":"publisher","first-page":"2740","DOI":"10.1109\/20.617715","volume":"33","author":"V.Yu. Krachkovsky","year":"1997","unstructured":"Krachkovsky, V.Yu. and Lee, Y.X. Decoding for Iterative Reed\u2013Solomon Coding Schemes, IEEE Trans. Magn., 1997, vol. 33, no. 5, pp. 2740\u20132742.","journal-title":"IEEE Trans. Magn."},{"key":"4239_CR26","volume-title":"Proc. 7th Int. ITG Conference on Source and Channel Coding (SCC\u201908), Ulm, Germany, Jan. 14\u201316","author":"V.R. Sidorenko","year":"2008","unstructured":"Sidorenko, V.R. Schmidt, G., and Bossert, M., Decoding Punctured Reed\u2013Solomon Codes up to the Singleton Bound, in Proc. 7th Int. ITG Conference on Source and Channel Coding (SCC\u201908), Ulm, Germany, Jan. 14\u201316, 2008."},{"key":"4239_CR27","first-page":"77","volume-title":"Proc. 2011 IEEE 26th Annual Conf. on Computational Complexity (CCC\u201911), San Jose, CA,USA, June 8\u201311","author":"V. Guruswami","year":"2011","unstructured":"Guruswami, V. Linear-Algebraic List Decoding of Folded Reed\u2013Solomon Codes, in Proc. 2011 IEEE 26th Annual Conf. on Computational Complexity (CCC\u201911), San Jose, CA,USA, June 8\u201311, 2011, pp. 77\u201385."},{"issue":"5","key":"4239_CR28","doi-asserted-by":"publisher","first-page":"1274","DOI":"10.1109\/18.133246","volume":"37","author":"G.-L. Feng","year":"1991","unstructured":"Feng, G.-L. and Tzeng, K.K. A Generalization of the Berlekamp\u2013Massey Algorithm for Multisequence Shift-Register Synthesis with Applications to Decoding Cyclic Codes, IEEE Trans. Inform. Theory, 1991, vol. 37, no. 5, pp. 1274\u20131287.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"4","key":"4239_CR29","doi-asserted-by":"publisher","first-page":"667","DOI":"10.3934\/amc.2011.5.667","volume":"5","author":"A. Zeh","year":"2011","unstructured":"Zeh, A. and Wachter, A. Fast Multi-Sequence Shift-Register Synthesis with the Euclidean Algorithm, Adv. Math. Commun., 2011, vol. 5, no. 4, pp. 667\u2013680.","journal-title":"Adv. Math. Commun."},{"key":"4239_CR30","volume-title":"The Theory of Error-Correcting Codes","author":"F.J. MacWilliams","year":"1977","unstructured":"MacWilliams, F.J. and Sloane, N.J.A. The Theory of Error-Correcting Codes, Amsterdam: North-Holland, 1977. Translated under the title Teoriya kodov, ispravlyayushchikh oshibki, Moscow: Svyaz\u2019, 1979."},{"key":"4239_CR31","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1109\/ISIT.2013.6620201","volume-title":"Proc. 2013 IEEE Int. Sympos. on Information Theory (ISIT\u20192013), Istanbul, Turkey, July 7\u201312","author":"A. Zeh","year":"2013","unstructured":"Zeh, A. Wachter-Zeh, A., Gadouleau, M., and Bezzateev, S.V., Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes, in Proc. 2013 IEEE Int. Sympos. on Information Theory (ISIT\u20192013), Istanbul, Turkey, July 7\u201312, 2013, pp. 126\u2013130."},{"key":"4239_CR32","first-page":"55","volume-title":"Proc. 1988 IEEE Int Sympos. on Information Theory (ISIT\u201998), Cambridge, MA,USA, Aug. 16\u201321","author":"V.Yu. Krachkovsky","year":"1998","unstructured":"Krachkovsky, V.Yu. and Lee, Y.X. Decoding of Parallel Reed\u2013Solomon Codes with Applications to Product and Concatenated Codes, in Proc. 1988 IEEE Int Sympos. on Information Theory (ISIT\u201998), Cambridge, MA,USA, Aug. 16\u201321, 1998. pp. 55."},{"issue":"7","key":"4239_CR33","doi-asserted-by":"publisher","first-page":"2991","DOI":"10.1109\/TIT.2009.2021308","volume":"55","author":"G. Schmidt","year":"2009","unstructured":"Schmidt, G. Sidorenko, V.R., and Bossert, M., Collaborative Decoding of Interleaved Reed\u2013Solomon Codes and Concatenated Code Designs, IEEE Trans. Inform. Theory, 2009, vol. 55, no. 7, pp. 2991\u20133012.","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"5","key":"4239_CR34","doi-asserted-by":"publisher","first-page":"1432","DOI":"10.1137\/090778274","volume":"40","author":"P. Gopalan","year":"2011","unstructured":"Gopalan, P. Guruswami, V., and Raghavendra, P., List Decoding Tensor Products and Interleaved Codes, SIAM J. Comput., 2011, vol. 40, no. 5, pp. 1432\u20131462.","journal-title":"SIAM J. Comput."}],"container-title":["Problems of Information Transmission"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0032946015030023.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0032946015030023","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1134\/S0032946015030023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0032946015030023.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T02:20:01Z","timestamp":1775010001000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0032946015030023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["4239"],"URL":"https:\/\/doi.org\/10.1134\/s0032946015030023","relation":{},"ISSN":["0032-9460","1608-3253"],"issn-type":[{"value":"0032-9460","type":"print"},{"value":"1608-3253","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7]]},"assertion":[{"value":"22 November 2013","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2015","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 October 2015","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}