Sequence of Numbers of Linear Codes with Increasing Hull Dimensions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909704789164032 |
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| author | Bouyuklieva, Stefka Bouyukliev, Iliya Özbudak, Ferruh |
| author_facet | Bouyuklieva, Stefka Bouyukliev, Iliya Özbudak, Ferruh |
| contents | The hull of a linear code $C$ is the intersection of $C$ with its dual code. We present and analyze the number of linear $q$-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given dimension $k$ and length $n\ge 2k$ the number of all $[n,k]_q$ linear codes with hull dimension $l$ decreases as $l$ increases. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length $n$ and dimension $k$, comparing the obtained numbers with the number of all linear codes for the given $n$ and $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sequence of Numbers of Linear Codes with Increasing Hull Dimensions Bouyuklieva, Stefka Bouyukliev, Iliya Özbudak, Ferruh Information Theory Discrete Mathematics 94B05 E.4 The hull of a linear code $C$ is the intersection of $C$ with its dual code. We present and analyze the number of linear $q$-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given dimension $k$ and length $n\ge 2k$ the number of all $[n,k]_q$ linear codes with hull dimension $l$ decreases as $l$ increases. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length $n$ and dimension $k$, comparing the obtained numbers with the number of all linear codes for the given $n$ and $k$. |
| title | Sequence of Numbers of Linear Codes with Increasing Hull Dimensions |
| topic | Information Theory Discrete Mathematics 94B05 E.4 |
| url | https://arxiv.org/abs/2402.01255 |