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A bound for the maximum weight of a linear code

Author
Ball, S.; Blokhuis, A.
Type of activity
Journal article
Journal
SIAM journal on discrete mathematics
Date of publication
2013-03-21
Volume
27
Number
1
First page
575
Last page
583
DOI
https://doi.org/10.1137/120880100 Open in new window
Repository
http://hdl.handle.net/2117/24092 Open in new window
Abstract
It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d, and maximum weight m satisfy a certain congruence relation. In the case that q = p is a prime, this leads to the bound m &le (n-d)p-e(p-1), where e {0, 1,.., k-2} is maximal with the property that (n-de) 0 (mod pk-1-e). Thus, if C contains a codeword of weight n, then n-d/(p-1)+d+e. The results obtained for linear codes are translated into corresponding results for (n, t)-arcs and t-fold blocking...
Citation
Ball, S.; Blokhuis, A. A bound for the maximum weight of a linear code. "SIAM journal on discrete mathematics", 21 Març 2013, vol. 27, núm. 1, p. 575-583.
Keywords
Mathematical techniques
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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