Construction of Additive Complementary Dual Codes Over Finite Fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912657786798080 |
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| author | Verma, Gyanendra K. Sharma, R. K. |
| author_facet | Verma, Gyanendra K. Sharma, R. K. |
| contents | In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields $\mathbb{F}_{q^2}$ with respect to the trace inner products, where $q$ is a prime power. First, we associate an additive code with a matrix known as a generator matrix. After that, we describe ACD codes in terms of generator matrices for the trace Hermitian and the trace Euclidean inner products. We also construct ACD codes over $\mathbb{F}_{q^2}$ from linear codes over $\mathbb{F}_q.$ Additionally, we present techniques for constructing ACD codes with various parameters from a given ACD code over $\mathbb{F}_{q^2}.$ By applying these methods, we construct numbers of trace Euclidean and trace Hermitian ACD codes that exhibit better parameters compared to the best known linear codes over $\mathbb{F}_9$ and $\mathbb{F}_4$ of the same size and length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11791 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Construction of Additive Complementary Dual Codes Over Finite Fields Verma, Gyanendra K. Sharma, R. K. Information Theory In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields $\mathbb{F}_{q^2}$ with respect to the trace inner products, where $q$ is a prime power. First, we associate an additive code with a matrix known as a generator matrix. After that, we describe ACD codes in terms of generator matrices for the trace Hermitian and the trace Euclidean inner products. We also construct ACD codes over $\mathbb{F}_{q^2}$ from linear codes over $\mathbb{F}_q.$ Additionally, we present techniques for constructing ACD codes with various parameters from a given ACD code over $\mathbb{F}_{q^2}.$ By applying these methods, we construct numbers of trace Euclidean and trace Hermitian ACD codes that exhibit better parameters compared to the best known linear codes over $\mathbb{F}_9$ and $\mathbb{F}_4$ of the same size and length. |
| title | Construction of Additive Complementary Dual Codes Over Finite Fields |
| topic | Information Theory |
| url | https://arxiv.org/abs/2302.11791 |