Bounds on Box Codes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912182319448064 |
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| author | Langberg, Michael Schwartz, Moshe Tamo, Itzhak |
| author_facet | Langberg, Michael Schwartz, Moshe Tamo, Itzhak |
| contents | Let $n_q(M,d)$ be the minimum length of a $q$-ary code of size $M$ and minimum distance $d$. Bounding $n_q(M,d)$ is a fundamental problem that lies at the heart of coding theory. This work considers a generalization $n^\bx_q(M,d)$ of $n_q(M,d)$ corresponding to codes in which codewords have \emph{protected} and \emph{unprotected} entries; where (analogs of) distance and of length are measured with respect to protected entries only. Such codes, here referred to as \emph{box codes}, have seen prior studies in the context of bipartite graph covering. Upper and lower bounds on $n^\bx_q(M,d)$ are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds on Box Codes Langberg, Michael Schwartz, Moshe Tamo, Itzhak Information Theory Combinatorics Let $n_q(M,d)$ be the minimum length of a $q$-ary code of size $M$ and minimum distance $d$. Bounding $n_q(M,d)$ is a fundamental problem that lies at the heart of coding theory. This work considers a generalization $n^\bx_q(M,d)$ of $n_q(M,d)$ corresponding to codes in which codewords have \emph{protected} and \emph{unprotected} entries; where (analogs of) distance and of length are measured with respect to protected entries only. Such codes, here referred to as \emph{box codes}, have seen prior studies in the context of bipartite graph covering. Upper and lower bounds on $n^\bx_q(M,d)$ are presented. |
| title | Bounds on Box Codes |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2501.05593 |