ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn

In this work, we study the structure of cyclic zero divisor codes over a family of group rings. We determine the number of elements of these codes and introduce the dual codes. Moreover, we show that there is no non-free cyclic LCD ℤ4 codes.

Keywords:

Group rings, cyclic codes zero divisors, linear complementary dual (LCD) codes.,

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[1] Beelen P, Jin L., (2018). Explicit MDS codes with complementary duals: IEEE Trans Inform Theory, 64: 7188-7193.
[2] Carlet C., Guilley S., (2014). Complementary dual codes for counter-measures to side-channel attacks: In Coding Theory and Applications: CIM Series in Mathematical Sciences, 3: 97-105.
[3] Carlet C., Mesnager S., Tang C., Qi Y., (2018). Euclidean and Hermitian LCD MDS codes: Design Code Cryptogr, 86: 2605-2618.
[4] Chen B., Dinh H.Q., Liu H., (2015). Repeated-root constacyclic codes of length Finite Fields Th App, 33: 137-159.
[5] Chen B., Liu H., (2017). New constructions of MDS codes with complementary duals: IEEE Trans Inform Theory, 64: 5776 - 5782.
[6] Dougherty S.T., Kim J.L., Ozkaya B., Sok L., Solé P., (2017). The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices: Int J Inf Coding Theory, 4: 116-128.
[7] Esmaeili M., Yari S., (2009) On complementary-dual quasi-cyclic codes: Finite Fields Th App, 15: 375-386.
[8] Galvez L., Kim J.L., Lee N., Roe Y.G., Won B.S., (2017). Some bounds on binary LCD codes: Cryptogr Commun, 10: 719-728.
[9] Hurley P., Hurley T., (2009). Codes from zero-divisors and units in group rings: Int J Inf Coding Theory, 1: 57-87.
[10] Jin L., (2017). Construction of MDS codes with complementary duals: IEEE Trans Inform Theory, 63: 2843-2847.
[11] Köroğlu, M.E., (2019). LCD codes and LCP of codes from units of group rings: Sakarya University Journal of Science, 23: 486-492.
[12] Li C., (2018). Hermitian LCD codes from cyclic codes: Design Code Cryptogr, 86: 2261-2278.
[13] Li C., Ding C., Li S., (2017). LCD cyclic codes over finite fields: IEEE Trans Inform Theory, 63: 4344-4356.
[14] Li S., Li C., Ding C., Liu H., (2017). Two families of LCD BCH codes: IEEE Trans Inform Theory, 63: 5699-5717.
[15] Liu X., Liu H., (2015). LCD codes over finite chain rings: Finite Fields Th App, 34: 1-19.
[16] Massey J.L., (1992). Linear codes with complementary duals: Discrete Math, 106: 337-342.
[17] Massey J.L., (1964). Reversible codes: Inform and Control, 7: 369-380.
[18] Milies C.P., Sehgal S.K., An introduction to group rings: Springer, 2002.
[19] Pang B., Zhu S., Sun Z., (2018). On LCD negacyclic codes over finite fields: Syst Sci Complex, 31: 1065-1077.
[20] Sendrier N., (2004). Linear codes with complementary duals meet the Gilbert-Varshamov bound: Discrete Math, 285: 345-347.
[21] Sok L., Shi M., Solé P., (2018). Construction of optimal LCD codes over large finite fields: Finite Fields Th App., 50: 138-153.
[22] Yang X., Massey J.L., (1994). The condition for a cyclic code to have a complementary dual: Discrete Math., 126: 391-393.

Sigma Mühendislik ve Fen Bilimleri Dergisi-Cover

ISSN: 1304-7191
Yayın Aralığı: Yılda 4 Sayı
Yayıncı: Yıldız Teknik Üniversitesi

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