Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.

Castillo-Guillén, C. A.; Álvarez-García, C.

doi:10.2478/auom-2021-0017

Abstract

Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given.

References

[1] A. Bayram, E. S. Oztas, I. Siap, Codes over 𝔽4 + ν𝔽4 and some DNA applications, Des. Codes Cryptogr. 80 379-393 (2016)10.1007/s10623-015-0100-8
Search in Google Scholar Back to article
[2] C. A. Castillo-Guillén, C. Rentería-Márquez, H. Tapia-Recillas, Consta-cyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, Finite Fields Appl. 43 1-21 (2017)10.1016/j.ffa.2016.08.004
Search in Google Scholar Back to article
[3] C. A. Castillo-Guillén, C. Rentería-Márquez, H. Tapia-Recillas, Duals of constacyclic codes over finite local Frobenius non-chain rings of length 4, Discrete Math. 341 919-933 (2018)10.1016/j.disc.2017.12.014
Search in Google Scholar Back to article
[4] C. A. Castillo-Guillén, C. Rentería-Márquez, E. Sarmiento-Rosales, H. Tapia-Recillas, R. H. Villareal, The dual of a constacyclic code, self dual and reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings of nilpotency index 3, Discrete Math. 342 2283-2296 (2019)10.1016/j.disc.2019.05.001
Search in Google Scholar Back to article
[5] C. A. Castillo-Guillén, C. Rentería-Márquez, Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4, An. Stiint. Univ. Ovidius Constanta Ser. Mat. (to appear)
Search in Google Scholar Back to article
[6] H. Q. Dinh, S. R. López-Permouth, Cyclic and Negacyclic Codes Over Finite Chain Rings, IEEE Trans. Inf. Theory 50 1728-1744 (2004)10.1109/TIT.2004.831789
Search in Google Scholar Back to article
[7] A. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane, P. Solé, The ℤ4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inf. Theory 40 301-319 (1994)10.1109/18.312154
Search in Google Scholar Back to article
[8] J. Kaur, R. Sehmi, S. Dutt, Reversible complement cyclic codes over Galois rings with applications to DNA codes, Discrete Appl. Math. 280 162-170 (2020)10.1016/j.dam.2020.01.004
Search in Google Scholar Back to article
[9] X. Liu, H. Liu, LCD codes over finite chain rings, Finite Fields Appl. 34 1-19 (2015)10.1016/j.ffa.2015.01.004
Search in Google Scholar Back to article
[10] J. L. Massey, Reversible codes, Inf. control 7 369-380 (1964)10.1016/S0019-9958(64)90438-3
Search in Google Scholar Back to article
[11] J. L. Massey, Linear codes with complementary duals, Discrete Math. 106/107 337-342 (1992)10.1016/0012-365X(92)90563-U
Search in Google Scholar Back to article
[12] B. R. McDonald, Finite Rings with Identity, Marcel Dekker, New York, 1974
Search in Google Scholar Back to article
[13] N. Sendrier, Linear codes with complementary dual meet the Gilbert-Varshamov bound, Discrete Math. 285 345-347 (2004)10.1016/j.disc.2004.05.005
Search in Google Scholar Back to article
[14] M. Shi, D. Huang, L. Sok, P. Solé, Double circulant LCD codes over ℤ4, Finite Fields Appl. 58 133-144 (2019)10.1016/j.ffa.2019.04.001
Search in Google Scholar Back to article
[15] J. Wood, Duality for modules over finite rings and applications to coding theory. Amer. J. Math. 121 555-575 (1999)10.1353/ajm.1999.0024
Search in Google Scholar Back to article
[16] X. Yang and J. L. Massey, The condition for a cyclic code to have a complementary dual, Discrete Math. 126 391-393 (1994)10.1016/0012-365X(94)90283-6
Search in Google Scholar Back to article
[17] B. Yildiz, I. Siap, Cyclic codes over 𝔽2[u]/〈u4 – 1〉 and applications to DNA codes, Comput. Math. Appl. 63 1169-1176 (2012)10.1016/j.camwa.2011.12.029
Search in Google Scholar Back to article

Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.

Abstract

Paradigm

My account