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A bound for the maximum weight of a linear code

Autor
Ball, S.; Blokhuis, A.
Tipus d'activitat
Article en revista
Revista
SIAM journal on discrete mathematics
Data de publicació
2013-03-21
Volum
27
Número
1
Pàgina inicial
575
Pàgina final
583
DOI
https://doi.org/10.1137/120880100 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/24092 Obrir en finestra nova
Resum
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...
Citació
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.
Paraules clau
Mathematical techniques
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants