Linear complementary pairs (LCPs) of codes have been studied since they were introduced in the context of discussing mitigation measures against possible hardware attacks to integrated circuits. Since the security parameters for LCPs of codes are defined from the (Hamming) distance and the dual distance of the codes in the pair, and the additional algebraic structure of skew constacyclic codes provides tools for studying the the dual and the distance of a code, we study the properties of LCPs of skew constacyclic codes. As a result, we give a characterization for those pairs, as well as multiple results that lead to constructing pairs with designed security parameters. We extend skew BCH codes to a constacyclic context and show that an LCP of codes can be immediately constructed from a skew BCH constacyclic code. Additionally, we describe a Hamming weight-preserving automorphism group in the set of skew constacyclic codes, which can be used for constructing LCPs of codes.

翻译：自线性互补对（LCP）码在集成电路硬件攻击缓解措施的研究背景下被提出以来，一直受到广泛关注。由于LCP码的安全参数由码对中两个码的（汉明）距离及其对偶距离共同定义，而斜常循环码的额外代数结构为研究码的对偶和距离提供了有效工具，因此本文对斜常循环码LCP的性质进行了研究。我们给出了此类码对的刻画特征，并提出了多种可构建具有预设安全参数的码对的方法。我们将斜BCH码推广至常循环结构，证明了利用斜BCH常循环码可直接构造LCP码。此外，我们描述了斜常循环码集上保持汉明权重的自同构群，该群可用于进一步构建LCP码。