Bounds on $k$-hash distances and rates of linear codes
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912656327180288 |
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| author | Della Fiore, Stefano Dalai, Marco |
| author_facet | Della Fiore, Stefano Dalai, Marco |
| contents | In this paper, we bound the rate of linear codes in $\mathbb{F}_q^n$ with the property that any $k\leq q$ codewords are all simultaneously distinct in at least $d_k$ coordinates. For the case of particular interest $q=k=3$ we recover, with a simpler proof, state of the art results in the case $d_3=1$ and new bounds for $d_3>1$. We finally discuss some related open problems on the list-decoding zero-error capacity of discrete memoryless channels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds on $k$-hash distances and rates of linear codes Della Fiore, Stefano Dalai, Marco Information Theory Combinatorics In this paper, we bound the rate of linear codes in $\mathbb{F}_q^n$ with the property that any $k\leq q$ codewords are all simultaneously distinct in at least $d_k$ coordinates. For the case of particular interest $q=k=3$ we recover, with a simpler proof, state of the art results in the case $d_3=1$ and new bounds for $d_3>1$. We finally discuss some related open problems on the list-decoding zero-error capacity of discrete memoryless channels. |
| title | Bounds on $k$-hash distances and rates of linear codes |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2505.05239 |