环 F q[u,v]/ 〈u2-1,v3-v,uv-vu〉上的斜循环码

doi:10.3969/j.issn.0253-2778.2017.10.009

中国科学技术大学学报 ›› 2017, Vol. 47 ›› Issue (10): 862-868.DOI: 10.3969/j.issn.0253-2778.2017.10.009

环 F q[u,v]/ 〈u2-1,v3-v,uv-vu〉上的斜循环码

管玥，刘艳，施敏加，卢振宇，吴波

安徽大学数学科学学院,安徽合肥 230601

收稿日期:2016-06-09 修回日期:2017-01-07 出版日期:2017-10-31 发布日期:2017-10-31

Skew cyclic codes over F q[u,v]/〈u2-1, v3-v, uv-vu〉

GUAN Yue, LIU Yan, SHI Minjia, LU Zhenyu, WU Bo

School of Mathematical Sciences, Anhui University. Hefei 230601, China

Received:2016-06-09 Revised:2017-01-07 Online:2017-10-31 Published:2017-10-31
Contact: SHI Minjia
About author:GUAN Yue, female, born in 1994, Master candidate. Research field: algebra code. E-mail: guanyueeee@163.com
Supported by:
Supported by NNSF of China (61672036), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (05015133), the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2015D11) and Key projects of support program for outstanding young talents in Colleges and Universities (gxyqZD2016008), Natural Science Research Project of Higher Education of Anhui Province of China(KJ2015JD18).

摘要/Abstract

摘要： 研究了环 R=

关键词: 线性码, 对偶码, 斜循环码, Gray 映射

Abstract: The skew cyclic codes over R=

Key words: linear codes, dual codes, skew cyclic codes, gray map

中图分类号:

TN911.22

管玥，刘艳，施敏加，卢振宇，吴波. 环 F q[u,v]/ 〈u2-1,v3-v,uv-vu〉上的斜循环码[J]. 中国科学技术大学学报, 2017, 47(10): 862-868.

GUAN Yue, LIU Yan, SHI Minjia, LU Zhenyu, WU Bo. Skew cyclic codes over F q[u,v]/〈u2-1, v3-v, uv-vu〉[J]. Journal of University of Science and Technology of China, 2017, 47(10): 862-868.

［1］
BOUCHER D, GEISELMANN W, ULMER F. Skew-cyclic codes[J]. Applicable Algebra Engineering Communication & Computing, 2007, 18(4) 379-389.
[2] BOUCHER D, ULMER F. Coding with skew polynomial ring[J]. Journal of Symbolic Computation, 2009, 44(12): 1644-1656.
[3] CAO Y L. Quasi-cyclic codes of index 2 and skew polynomial rings over finite fields[J]. Finite Fieids and Their Applications, 2014, 27: 143-158.
[4] BOUCHER D, ULMER F. Self-dual skew codes and factorization of skew polynomials[J]. Journal of Symbolic Computation, 2014, 60(1): 47-61.
[5] ABUALRUB T, GHRAYEB A, AYDIN N, et al. On the construction of skew quasi-cyclic codes[J]. IEEE Transactions on Information Theory, 2010, 56(5): 2081-2090.
[6] JITMAN S, LING S, UDOMKAVANICH P. Skew constacyclic codes over finite chain rings[J]. Advances in Mathematics Communications, 2010, 6(1): 39-63.
[7] AYDIN N, ABUALRUB T, SENEVIRATNE P. On θ-cyclic codes over F2+vF2[J]. Australian Journal of Combinatorics, 2012, 54: 115-126.
[8] GAO J. Skew cyclic codes over Fp + vFp[J]. Journal of applied mathematics & informatics, 2013, 31(3-4): 337-342.
[9] GURSOY F, SIAP I, YILDIZ B. Construction of skew cyclic codes over Fq+vFq[J]. Advances in Mathematics of Communications, 2014, 8(3): 313-322.
[10] ASHRAF M, GHULAM M. On skew cyclic codes over F3 + vF3[J]. International Journal of Information & Coding Theory, 2014, 2(4): 218-225.
[11] SHI M J, YAO T, ALAHMADI A, et al. Skew cyclic codes over Fp+vFp+v2Fq[J]. The Institute of Electronics, Information and Communication Engineers, 2015, 98(8): 1845-1848.
[12] YAO T, SHI M J, SOL P. Skew cyclic codes over Fp +u Fp +vFq +uvFq[J]. Journal of Algebra Combinatorics Discrete Structures & Applications, 2015, 2(3): 163-168.
[13] SIAP I, ABUALRUB T, AYDIN N, et al. Skew cyclic codes of arbitrary length[J]. International Journal of Information & Coding Theory, 2011, 2(1): 10-20.

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环 F q[u,v]/ 〈u2-1,v3-v,uv-vu〉上的斜循环码

Skew cyclic codes over F q[u,v]/〈u2-1, v3-v, uv-vu〉

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