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 $$d(D^\bot )$$ . It has been recently shown that if C and D are both 2-sided group codes over a finite field, then C and $$D^\bot $$ are permutation equivalent. Hence the security parameter for an LCP of 2-sided group codes (C, D) is simply d(C). We extend this result to 2-sided group codes over finite chain rings.

中文翻译：

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有限链环上的线性互补群码对

有限域上的线性互补对偶 (LCD) 码和线性互补对 (LCP) 码由于它们在密码学中的应用，在旁道和故障注入攻击的背景下，最近得到了深​​入研究。代码 (C, D) 的 LCP 的安全参数定义为最小距离 d(C) 和 $$d(D^\bot )$$ 中的最小值。最近已经表明，如果 C 和 D 都是有限域上的 2 边群码，那么 C 和 $$D^\bot $$ 是置换等价的。因此，2 边组代码 (C, D) 的 LCP 的安全参数只是 d(C)。我们将此结果扩展到有限链环上的 2 边群码。