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

Mehmet Emin Köroğlu; Bayram Ali Ersoy

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

Abstract

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

References

[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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Mehmet Emin Köroğlu This is me
0000-0002-9173-4944
Türkiye

Bayram Ali Ersoy This is me
0000-0002-8307-9644
Türkiye

Publication Date

June 1, 2019

Submission Date

April 10, 2019

Acceptance Date

May 19, 2019

Published in Issue

Year 2019 Volume: 37 Number: 2

IZ

https://izlik.org/JA68UR43ML

Cite

RIS / Bibtex

APA

Köroğlu, M. E., & Ersoy, B. A. (2019). ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn. Sigma Journal of Engineering and Natural Sciences, 37(2), 541-549. https://izlik.org/JA68UR43ML

AMA

1.Köroğlu ME, Ersoy BA. ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn. SIGMA. 2019;37(2):541-549. https://izlik.org/JA68UR43ML

Chicago

Köroğlu, Mehmet Emin, and Bayram Ali Ersoy. 2019. “ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn”. Sigma Journal of Engineering and Natural Sciences 37 (2): 541-49. https://izlik.org/JA68UR43ML.

EndNote

Köroğlu ME, Ersoy BA (June 1, 2019) ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn. Sigma Journal of Engineering and Natural Sciences 37 2 541–549.

IEEE

[1]M. E. Köroğlu and B. A. Ersoy, “ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn”, SIGMA, vol. 37, no. 2, pp. 541–549, June 2019, [Online]. Available: https://izlik.org/JA68UR43ML

ISNAD

Köroğlu, Mehmet Emin - Ersoy, Bayram Ali. “ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn”. Sigma Journal of Engineering and Natural Sciences 37/2 (June 1, 2019): 541-549. https://izlik.org/JA68UR43ML.

JAMA

1.Köroğlu ME, Ersoy BA. ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn. SIGMA. 2019;37:541–549.

MLA

Köroğlu, Mehmet Emin, and Bayram Ali Ersoy. “ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 2, June 2019, pp. 541-9, https://izlik.org/JA68UR43ML.

Vancouver

1.Mehmet Emin Köroğlu, Bayram Ali Ersoy. ON CYCLIC CODES AND CYCLIC LCD CODES FROM THE FAMILY OF GROUP RINGS ℤ4Cn. SIGMA [Internet]. 2019 Jun. 1;37(2):541-9. Available from: https://izlik.org/JA68UR43ML