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| Autori principali: | , , |
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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.14848 |
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| _version_ | 1866914606384939008 |
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| author | Liu, Haibo Guo, Xin Liao, Qunying |
| author_facet | Liu, Haibo Guo, Xin Liao, Qunying |
| contents | Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions have been interesting in coding theory and cryptography. In this paper, a generic construction for ternary linear codes with dimension $m+2$ is presented, where $m$ is an integer, and a necessary and sufficient condition for this ternary linear code to be minimal is derived. Based on this condition and Krawtchouk Polynomials, a new class of minimal ternary linear codes violating the Ashikhmin-Barg condition are obtained, and then their complete weight enumerators are determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14848 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of Minimal Ternary Linear Codes with Dimension $m+2$ Via Krawtchouk Polynomials Liu, Haibo Guo, Xin Liao, Qunying Information Theory Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions have been interesting in coding theory and cryptography. In this paper, a generic construction for ternary linear codes with dimension $m+2$ is presented, where $m$ is an integer, and a necessary and sufficient condition for this ternary linear code to be minimal is derived. Based on this condition and Krawtchouk Polynomials, a new class of minimal ternary linear codes violating the Ashikhmin-Barg condition are obtained, and then their complete weight enumerators are determined. |
| title | Construction of Minimal Ternary Linear Codes with Dimension $m+2$ Via Krawtchouk Polynomials |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.14848 |