Optimal Anticodes, Diameter Perfect Codes, Chains and Weights
| Autor: | Panek, Luciano, Panek, Nayene Michele Paião |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $P$ be a partial order on $[n] = \{1,2,\ldots,n\}$, $\mathbb{F}_{q}^n$ be the linear space of $n$-tuples over a finite field $\mathbb{F}_{q}$ and $w$ be a weight on $\mathbb{F}_{q}$. In this paper, we consider metrics on $\mathbb{F}_{q}^n$ induced by chain orders $P$ over $[n]$ and weights $w$ over $\mathbb{F}_q$, and we determine the cardinality of all optimal anticodes and completely classify them. Moreover, we determine all diameter perfect codes for a set of relevant instances on the aforementioned metric spaces. Comment: This work has been accepted for publication in the IEEE Transactions on Information Theory. Copyright (c) 2021 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org |
| Databáze: | arXiv |
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