{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:20:17Z","timestamp":1758280817406},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T00:00:00Z","timestamp":1611014400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T00:00:00Z","timestamp":1611014400000},"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":["AAECC"],"published-print":{"date-parts":[[2023,1]]},"DOI":"10.1007\/s00200-020-00472-6","type":"journal-article","created":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T13:02:56Z","timestamp":1611061376000},"page":"111-128","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the symbol-pair distance of some classes of repeated-root constacyclic codes over Galois ring"],"prefix":"10.1007","volume":"34","author":[{"given":"Hai Q.","family":"Dinh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Narendra","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abhay Kumar","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manoj Kumar","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Indivar","family":"Gupta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paravee","family":"Maneejuk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,1,19]]},"reference":[{"key":"472_CR1","doi-asserted-by":"publisher","first-page":"2126","DOI":"10.1109\/TIT.2003.815763","volume":"49","author":"T Abualrub","year":"2003","unstructured":"Abualrub, T., Oehmke, R.: On the generators of $${\\mathbb{Z}}_{4}$$ cyclic codes of length $$2^e$$. IEEE Trans. Inf. Theory 49, 2126\u20132133 (2003)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"#cr-split#-472_CR2.1","unstructured":"Berman S.D., Semisimple cyclic and Abelian codes. II, Kibernetika (Kiev) 3, 21-30 (1967) (in Rus-sian)"},{"key":"#cr-split#-472_CR2.2","unstructured":"English translation: Cybernetics 3, 17-23 (1967)"},{"key":"472_CR3","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1090\/S0273-0979-1993-00426-9","volume":"29","author":"AR Calderbank","year":"1993","unstructured":"Calderbank, A.R., Hammons, A.R., Kumar, P.V., Sloane, N.J.A., Sol\u00e9, P.: A linear construction for certain Kerdock and Preparata codes. Bull. Am. Math. Soc. 29, 218\u2013222 (1993)","journal-title":"Bull. Am. Math. Soc."},{"key":"472_CR4","doi-asserted-by":"crossref","unstructured":"Cassuto, Y., Blaum, M.: Codes for symbol-pair read channels. In: Conference in Proceedings IEEE International Symposium Information Theory, Austin, pp. 988\u2013992 (2010)","DOI":"10.1109\/ISIT.2010.5513753"},{"key":"472_CR5","doi-asserted-by":"publisher","first-page":"8011","DOI":"10.1109\/TIT.2011.2164891","volume":"57","author":"Y Cassuto","year":"2011","unstructured":"Cassuto, Y., Blaum, M.: Codes for symbol-pair read channels. IEEE Trans. Inf. Theory 57, 8011\u20138020 (2011)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR6","doi-asserted-by":"crossref","unstructured":"Cassuto, Y., Litsyn, S.: Symbol-pair codes: algebraic constructions and asymptotic bounds. In: Conference in Proceedings IEEE International Symposium on Information Theory, St. Petersburg, Russia, pp. 2348\u20132352 (2011)","DOI":"10.1109\/ISIT.2011.6033982"},{"key":"472_CR7","doi-asserted-by":"crossref","unstructured":"Chen, B., Lin, L., Liu, H.: Constacyclic symbol-pair codes: lower bounds and optimal constructions. arXiv:1605.03460 (2016)","DOI":"10.1109\/TIT.2017.2753250"},{"key":"472_CR8","doi-asserted-by":"publisher","first-page":"7259","DOI":"10.1109\/TIT.2013.2276615","volume":"59","author":"YM Chee","year":"2013","unstructured":"Chee, Y.M., Ji, L., Kiah, H.M., Wang, C., Yin, J.: Maximum distance separable codes for symbol-pair read channels. IEEE Trans. Inf. Theory 59, 7259\u20137267 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR9","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., Schoeller, P.A., von Seemann, N.: On repeated-root cyclic codes. IEEE Trans. Inform. Theory 37, 337\u2013342 (1991)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"472_CR10","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/BF01390768","volume":"6","author":"AR Calderbank","year":"1995","unstructured":"Calderbank, A.R., Sloane, N.J.A.: Modular and $$p$$-adic codes. Des. Codes Cryptogr. 6, 21\u201335 (1995)","journal-title":"Des. Codes Cryptogr."},{"key":"472_CR11","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/j.ffa.2017.10.002","volume":"49","author":"B Ding","year":"2018","unstructured":"Ding, B., Zhang, T., Ge, G.: Maximum distance separable codes for b-symbol read channels. Finite Fields Their Appl. 49, 180\u2013197 (2018)","journal-title":"Finite Fields Their Appl."},{"key":"472_CR12","doi-asserted-by":"crossref","unstructured":"Dinh, H.Q.: On some classes of repeated-root constacyclic codes of length a power of 2 over Galois rings. In: Trends Math, pp. 131\u2013147 (2010)","DOI":"10.1007\/978-3-0346-0286-0_10"},{"key":"472_CR13","first-page":"207","volume":"13","author":"HQ Dinh","year":"2011","unstructured":"Dinh, H.Q., Vo, T.M.: Repeated-root cyclic and negacyclic codes of prime power lengths with a finite commutative chain ring alphabet. East West J. Math. 13, 207\u2013224 (2011)","journal-title":"East West J. Math."},{"key":"472_CR14","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1090\/conm\/480\/09369","volume":"480","author":"HQ Dinh","year":"2009","unstructured":"Dinh, H.Q.: Repeated-root constacyclic codes of prime power length. AMS Contemp. Math. 480, 87\u2013100 (2009)","journal-title":"AMS Contemp. Math."},{"key":"472_CR15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2726691","author":"HQ Dinh","year":"2017","unstructured":"Dinh, H.Q., Nguyen, B.T., Singh, A.K., Sriboonchitta, S.: On the symbol-pair distance of repeated-root constacyclic codes of prime power lengths. IEEE Trans. Inform. Theory (2017). https:\/\/doi.org\/10.1109\/TIT.2017.2726691","journal-title":"IEEE Trans. Inform. Theory"},{"key":"472_CR16","doi-asserted-by":"publisher","first-page":"1730","DOI":"10.1109\/TIT.2009.2013015","volume":"55","author":"HQ Dinh","year":"2009","unstructured":"Dinh, H.Q.: Constacyclic codes of length $$2^s$$ over Galois extension rings of $${\\mathbb{F}}_{2} + u{\\mathbb{F}}_{2}$$. IEEE Trans. Inform. Theory 55, 1730\u20131740 (2009)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"472_CR17","doi-asserted-by":"publisher","first-page":"1728","DOI":"10.1109\/TIT.2004.831789","volume":"50","author":"HQ Dinh","year":"2004","unstructured":"Dinh, H.Q., L\u00f3pez-Permouth, S.R.: Cyclic and negacyclic codes over finite chain rings. IEEE Trans. Inform. Theory 50, 1728\u20131744 (2004)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"472_CR18","doi-asserted-by":"publisher","first-page":"940","DOI":"10.1016\/j.jalgebra.2010.05.027","volume":"324","author":"HQ Dinh","year":"2010","unstructured":"Dinh, H.Q.: Constacyclic codes of length $$p^s$$ over ring $$\\mathbb{F}_{p^m} + u\\mathbb{F}_{p^m}$$. J. Algebra 324, 940\u2013950 (2010)","journal-title":"J. Algebra"},{"key":"472_CR19","doi-asserted-by":"crossref","unstructured":"Dinh, H.Q.: Repeated root constacyclic codes of length $$2^s$$ over $${\\mathbb{Z}}_{2}^{a}$$. In: Algebra and Its Applications. Contemporary Mathematics American Mathematical Society, vol. 419, pp. 95\u2013110 (2006)","DOI":"10.1090\/conm\/419\/07998"},{"key":"472_CR20","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1109\/TIT.2006.887487","volume":"53","author":"HQ Dinh","year":"2007","unstructured":"Dinh, H.Q.: Complete distances of all negacyclic codes of length $$2^s$$ over $${{\\mathbb{Z}}}_{2^{a} }$$. IEEE Trans. Inform. Theory 53, 147\u2013161 (2007)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"472_CR21","doi-asserted-by":"publisher","first-page":"4252","DOI":"10.1109\/TIT.2005.859284","volume":"51","author":"HQ Dinh","year":"2005","unstructured":"Dinh, H.Q.: Negacyclic codes of length $$2^s$$ over Galois rings. IEEE Trans. Inf. Theory 51, 4252\u20134262 (2005)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR22","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.ffa.2016.09.004","volume":"43","author":"HQ Dinh","year":"2017","unstructured":"Dinh, H.Q., Liu, H., Liu, X., Sriboonchitta, S.: On structure and distances of some classes of repeated-root constacyclic codes over Galois rings. Finite Fields Appl. 43, 86\u2013105 (2017)","journal-title":"Finite Fields Appl."},{"key":"472_CR23","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.ffa.2007.07.001","volume":"14","author":"HQ Dinh","year":"2008","unstructured":"Dinh, H.Q.: On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions. Finite Fields Appl. 14, 22\u201340 (2008)","journal-title":"Finite Fields Appl."},{"key":"472_CR24","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1201\/9781420010961.ch10","volume":"248","author":"HQ Dinh","year":"2006","unstructured":"Dinh, H.Q.: Structure of some classes of repeated-root constacyclic codes over integers modulo $$2^m$$. Ser. Lect. Notes Pure Appl. Math. 248, 105\u2013117 (2006)","journal-title":"Ser. Lect. Notes Pure Appl. Math."},{"key":"472_CR25","first-page":"326","volume":"28","author":"G Falkner","year":"1979","unstructured":"Falkner, G., Kowol, B., Heise, W., Zehendner, E.: On the existence of cyclic optimal codes. Atti Semin. Mat. Fis. Univ. Modena 28, 326\u2013341 (1979)","journal-title":"Atti Semin. Mat. Fis. Univ. Modena"},{"key":"472_CR26","doi-asserted-by":"crossref","unstructured":"Hirotomo, M., Takita, M., Morii, M.: Syndrome decoding of symbol-pair codes. In: Conference in Proceedings IEEE Information Theory Workshop, Hobart, pp. 162\u2013166 (2014)","DOI":"10.1109\/ITW.2014.6970813"},{"key":"472_CR27","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1109\/18.312154","volume":"40","author":"AR Hammons Jr","year":"1994","unstructured":"Hammons Jr., A.R., Kumar, P.V., Calderbank, A.R., Sloane, N.J.A., Sol\u00e9, P.: The $${\\mathbb{Z}}_{4}$$-linearity of Kerdock, Preparata, Goethals, and related codes. IEEE Trans. Inf. Theory 40, 301\u2013319 (1994)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR28","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511807077","volume-title":"Fundamentals of Error-Correcting Codes","author":"WC Huffman","year":"2003","unstructured":"Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003)"},{"key":"472_CR29","doi-asserted-by":"publisher","first-page":"5828","DOI":"10.1109\/TIT.2015.2481889","volume":"61","author":"X Kai","year":"2015","unstructured":"Kai, X., Zhu, S., Li, P.: A construction of new MDS symbol-pair codes. IEEE Trans. Inf. Theory 61, 5828\u20135834 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR30","unstructured":"McDonald B.R.: Finite rings with identity. In: Pure and Applied Mathematics, vol. 28. Marcel Dekker, New York (1974)"},{"key":"472_CR31","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1109\/TIT.1973.1054936","volume":"19","author":"JL Massey","year":"1973","unstructured":"Massey, J.L., Costello, D.J., Justesen, J.: Polynomial weights and code constructions. IEEE Trans. Inf. Theory 19, 101\u2013110 (1973)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR32","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1109\/TIT.2003.811921","volume":"49","author":"CS Nedeloaia","year":"2003","unstructured":"Nedeloaia, C.S.: Weight distributions of cyclic self-dual codes. IEEE Trans. Inf. Theory 49, 1582\u20131591 (2003)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR33","volume-title":"Handbook of Coding Theory","author":"V Pless","year":"1998","unstructured":"Pless, V., Huffman, W.C.: Handbook of Coding Theory. Elsevier, Amsterdam (1998)"},{"key":"472_CR34","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1109\/TIT.1986.1057151","volume":"32","author":"RM Roth","year":"1986","unstructured":"Roth, R.M., Seroussi, G.: On cyclic MDS codes of length qover GF(q). IEEE Trans. Inf. Theory 32, 284\u2013285 (1986)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR35","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/j.dam.2005.03.016","volume":"154","author":"A S\u0103l\u0103gean","year":"2006","unstructured":"S\u0103l\u0103gean, A.: Repeated-root cyclic and negacyclic codes over finite chain rings. Discrete Appl. Math. 154, 413\u2013419 (2006)","journal-title":"Discrete Appl. Math."},{"key":"472_CR36","doi-asserted-by":"publisher","first-page":"732","DOI":"10.1109\/18.556131","volume":"43","author":"L Tang","year":"1997","unstructured":"Tang, L., Soh, C.B., Gunawan, E.: A note on the q-ary image of a $$q^m$$-ary repeated-root cyclic code. IEEE Trans. Inf. Theory 43, 732\u2013737 (1997)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR37","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1109\/18.75250","volume":"37","author":"JH Van Lint","year":"1991","unstructured":"Van Lint, J.H.: Repeated-root cyclic codes. IEEE Trans. Inform. Theory 37, 343\u2013345 (1991)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"472_CR38","first-page":"291","volume":"6","author":"Z Wan","year":"1999","unstructured":"Wan, Z.: Cyclic codes over Galois rings. Algebra Colloq. 6, 291\u2013304 (1999)","journal-title":"Algebra Colloq."},{"key":"472_CR39","doi-asserted-by":"crossref","unstructured":"Yaakobi, E., Bruck, J., Siegel, P.H.: Decoding of cyclic codes over symbol-pair read channels. In: Conference in Proceedings International Symposium Information Theory, Cambridge, pp. 2891\u20132895 (2012)","DOI":"10.1109\/ISIT.2012.6284053"},{"key":"472_CR40","doi-asserted-by":"publisher","first-page":"1541","DOI":"10.1109\/TIT.2016.2522434","volume":"62","author":"E Yaakobi","year":"2016","unstructured":"Yaakobi, E., Bruck, J., Siegel, P.H.: Constructions and decoding of cyclic codes over b-symbol read channels. IEEE Trans. Inf. Theory 62, 1541\u20131551 (2016)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"472_CR41","doi-asserted-by":"crossref","unstructured":"Yaakobi, E., Bruck, J., Siegel, P.H.: Decoding of cyclic codes over symbol-pair read channels. In: Conference in Proceedings of International Symposium Information Theory, Cambridge, pp. 2891\u20132895 (2012)","DOI":"10.1109\/ISIT.2012.6284053"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-020-00472-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00200-020-00472-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-020-00472-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T16:03:43Z","timestamp":1673453023000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00200-020-00472-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,19]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["472"],"URL":"https:\/\/doi.org\/10.1007\/s00200-020-00472-6","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,19]]},"assertion":[{"value":"13 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}