On the hull and complementarity of one generator quasi-cyclic codes and four-circulant codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910289239212032 |
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| author | Aliabadi, Zohreh Güneri, Cem Kalaycı, Tekgül |
| author_facet | Aliabadi, Zohreh Güneri, Cem Kalaycı, Tekgül |
| contents | We study one generator quasi-cyclic codes and four-circulant codes, which are also quasi-cyclic but have two generators. We state the hull dimensions for both classes of codes in terms of the polynomials in their generating elements. We prove results such as the hull dimension of a four-circulant code is even and one-dimensional hull for double-circulant codes, which are special one generator codes, is not possible when the alphabet size $q$ is congruent to 3 mod 4. We also characterize linear complementary pairs among both classes of codes. Computational results on the code families in consideration are provided as well. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_05449 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the hull and complementarity of one generator quasi-cyclic codes and four-circulant codes Aliabadi, Zohreh Güneri, Cem Kalaycı, Tekgül Information Theory 94B05 94B15 H.1.1 We study one generator quasi-cyclic codes and four-circulant codes, which are also quasi-cyclic but have two generators. We state the hull dimensions for both classes of codes in terms of the polynomials in their generating elements. We prove results such as the hull dimension of a four-circulant code is even and one-dimensional hull for double-circulant codes, which are special one generator codes, is not possible when the alphabet size $q$ is congruent to 3 mod 4. We also characterize linear complementary pairs among both classes of codes. Computational results on the code families in consideration are provided as well. |
| title | On the hull and complementarity of one generator quasi-cyclic codes and four-circulant codes |
| topic | Information Theory 94B05 94B15 H.1.1 |
| url | https://arxiv.org/abs/2307.05449 |