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Covering Radius of Matrix Codes Endowed with the Rank Metric
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| Title: | Covering Radius of Matrix Codes Endowed with the Rank Metric | Authors: | Byrne, Eimear; Ravagnani, Alberto | Permanent link: | http://hdl.handle.net/10197/8999 | Date: | 23-May-2017 | Online since: | 2017-10-10T11:38:55Z | Abstract: | In this paper we study properties and invariants of matrix codes endowed with the rank metric and relate them to the covering radius. We introduce new tools for the analysis of rank-metric codes, such as puncturing and shortening constructions. We give upper bounds on the covering radius of a code by applying different combinatorial methods. The various bounds are then applied to the classes of maximal-rank-distance and quasi-maximal-rank-distance codes. | Funding Details: | Swiss National Science Foundation | Type of material: | Journal Article | Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM Journal on Discrete Mathematics | Volume: | 31 | Issue: | 2 | Start page: | 927 | End page: | 944 | Copyright (published version): | 2017 Society for Industrial and Applied Mathematics | Keywords: | Rank metric code; Covering radius; Rank distance distribution; Rank coset weights; External distance bound; Dual distance bound; Initial set bound | DOI: | 10.1137/16M1091769 | Language: | en | Status of Item: | Peer reviewed | This item is made available under a Creative Commons License: | https://creativecommons.org/licenses/by-nc-nd/3.0/ie/ |
| Appears in Collections: | Mathematics and Statistics Research Collection |
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