Linear Complementary Pair Of Abelian Codes over Finite Chain Rings
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Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side-channel and fault injection attacks. The security parameter for an LCP of codes (C,D) is defined as the minimum of the minimum distances d(C) and d(D^). It has been recently shown that if C and D are both abelian codes over a finite field F_q, and the length of the codes is relatively prime to q, then C and D^ are equivalent. Hence the security parameter for an LCP of abelian codes (C,D) is simply d(C). In this work, we first extend this result to the non-semisimple case, i.e. the code length is divisible by the characteristic of the field of definition. Then we use the result over the finite fields to prove the same fact for an LCP of abelian codes over any finite chain ring.
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