Linear complementary pairs of skew constacyclic codes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917911488102400 |
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| author | Lobillo, F. J. Muñoz, José Manuel |
| author_facet | Lobillo, F. J. Muñoz, José Manuel |
| contents | 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. In this situation, the security parameters for LCPs of codes are defined as the (Hamming) distance and the dual distance of the codes in the pair. We study the properties of LCPs of skew constacyclic codes, since their algebraic structure provides tools for studying their duals and their distances. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07183 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linear complementary pairs of skew constacyclic codes Lobillo, F. J. Muñoz, José Manuel Information Theory Rings and Algebras 16S36, 94B60, 94B65 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. In this situation, the security parameters for LCPs of codes are defined as the (Hamming) distance and the dual distance of the codes in the pair. We study the properties of LCPs of skew constacyclic codes, since their algebraic structure provides tools for studying their duals and their distances. 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. |
| title | Linear complementary pairs of skew constacyclic codes |
| topic | Information Theory Rings and Algebras 16S36, 94B60, 94B65 |
| url | https://arxiv.org/abs/2312.07183 |