Self-Orthogonal Codes from Vectorial Dual-Bent Functions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911803460550656 |
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| author | Wang, Jiaxin Wei, Yadi Fu, Fang-Wei Li, Juan |
| author_facet | Wang, Jiaxin Wei, Yadi Fu, Fang-Wei Li, Juan |
| contents | Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In \cite{HLL2023Te,LH2023Se}, $p$-ary self-orthogonal codes were constructed by using $p$-ary weakly regular bent functions, where $p$ is an odd prime. In \cite{WH2023Se}, two classes of non-degenerate quadratic forms were used to construct $q$-ary self-orthogonal codes, where $q$ is a power of a prime. In this paper, we construct new families of $q$-ary self-orthogonal codes using vectorial dual-bent functions. Some classes of at least almost optimal linear codes are obtained from the dual codes of the constructed self-orthogonal codes. In some cases, we completely determine the weight distributions of the constructed self-orthogonal codes. From the view of vectorial dual-bent functions, we illustrate that the works on constructing self-orthogonal codes from $p$-ary weakly regular bent functions \cite{HLL2023Te,LH2023Se} and non-degenerate quadratic forms with $q$ being odd \cite{WH2023Se} can be obtained by our results. We partially answer an open problem on determining the weight distribution of a class of self-orthogonal codes given in \cite{LH2023Se}. As applications, we construct new infinite families of at least almost optimal $q$-ary linear complementary dual codes (for short, LCD codes) and quantum codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12578 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-Orthogonal Codes from Vectorial Dual-Bent Functions Wang, Jiaxin Wei, Yadi Fu, Fang-Wei Li, Juan Information Theory Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In \cite{HLL2023Te,LH2023Se}, $p$-ary self-orthogonal codes were constructed by using $p$-ary weakly regular bent functions, where $p$ is an odd prime. In \cite{WH2023Se}, two classes of non-degenerate quadratic forms were used to construct $q$-ary self-orthogonal codes, where $q$ is a power of a prime. In this paper, we construct new families of $q$-ary self-orthogonal codes using vectorial dual-bent functions. Some classes of at least almost optimal linear codes are obtained from the dual codes of the constructed self-orthogonal codes. In some cases, we completely determine the weight distributions of the constructed self-orthogonal codes. From the view of vectorial dual-bent functions, we illustrate that the works on constructing self-orthogonal codes from $p$-ary weakly regular bent functions \cite{HLL2023Te,LH2023Se} and non-degenerate quadratic forms with $q$ being odd \cite{WH2023Se} can be obtained by our results. We partially answer an open problem on determining the weight distribution of a class of self-orthogonal codes given in \cite{LH2023Se}. As applications, we construct new infinite families of at least almost optimal $q$-ary linear complementary dual codes (for short, LCD codes) and quantum codes. |
| title | Self-Orthogonal Codes from Vectorial Dual-Bent Functions |
| topic | Information Theory |
| url | https://arxiv.org/abs/2403.12578 |