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Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. LCD cyclic codes have been known as reversible cyclic codes that had applications in data storage. Due to a newly discovered application in cryptography, interest in LCD codes has increased again. Although LCD codes over finite fields have been extensively studied so far, little work has been done on LCD codes over chain rings. In this paper, we are interested in structure of LCD codes over chain rings. We show that LCD codes over chain rings are free codes. We provide some necessary and sufficient conditions for an LCD code $C$ over finite chain rings in terms of projections of linear codes. We also showed the existence of asymptotically good LCD codes over finite chain rings.
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참고문헌 (23)
참고문헌 신청
A. R. Calderbank / 1995 / Modular andp-adic cyclic codes / Designs, Codes and Cryptography 6(1):21~35
Claude Carlet / 2016 / Complementary dual codes for counter-measures to side-channel attacks / Advances in Mathematics of Communications 10(1):131~150
Claude Carlet / 2018 / Linear Codes Over $\mathbb F_q$ Are Equivalent to LCD Codes for $q>3$ / IEEE Transactions on Information Theory 64(4):3010~3017
Steven T. Dougherty / 2017 / The combinatorics of LCD codes: linear programming bound and orthogonal matrices / International Journal of Information and Coding Theory 4(2/3):116~128
M. Esmaeili / 2009 / On complementary-dual quasi-cyclic codes / Finite Fields and Their Applications 15(3):375~386
Claude Carlet / 2016 / Complementary dual codes for counter-measures to side-channel attacks / Advances in Mathematics of Communications 10(1):131~150
Claude Carlet / 2018 / Linear Codes Over $\mathbb F_q$ Are Equivalent to LCD Codes for $q>3$ / IEEE Transactions on Information Theory 64(4):3010~3017
Steven T. Dougherty / 2017 / The combinatorics of LCD codes: linear programming bound and orthogonal matrices / International Journal of Information and Coding Theory 4(2/3):116~128
M. Esmaeili / 2009 / On complementary-dual quasi-cyclic codes / Finite Fields and Their Applications 15(3):375~386
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