Construction of Minimal Binary Linear Codes of dimension $n+3$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916167317192704 |
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| author | Shaikh, Wajid M. Jain, Rupali S. Reddy, B. Surendranath Patil, Bhagyashri S. |
| author_facet | Shaikh, Wajid M. Jain, Rupali S. Reddy, B. Surendranath Patil, Bhagyashri S. |
| contents | In this paper, we will give the generic construction of a binary linear code of dimension $n+3$ and derive the necessary and sufficient conditions for the constructed code to be minimal. Using generic construction, a new family of minimal binary linear code will be constructed from a special class of Boolean functions violating the Ashikhmin-Barg condition. We also obtain the weight distribution of the constructed minimal binary linear code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of Minimal Binary Linear Codes of dimension $n+3$ Shaikh, Wajid M. Jain, Rupali S. Reddy, B. Surendranath Patil, Bhagyashri S. Information Theory Rings and Algebras 94B05, 94C10, 94A60 In this paper, we will give the generic construction of a binary linear code of dimension $n+3$ and derive the necessary and sufficient conditions for the constructed code to be minimal. Using generic construction, a new family of minimal binary linear code will be constructed from a special class of Boolean functions violating the Ashikhmin-Barg condition. We also obtain the weight distribution of the constructed minimal binary linear code. |
| title | Construction of Minimal Binary Linear Codes of dimension $n+3$ |
| topic | Information Theory Rings and Algebras 94B05, 94C10, 94A60 |
| url | https://arxiv.org/abs/2403.13350 |