Limitantes para Códigos de Peso Constante
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Data
2011-01-28
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Universidade Federal de Goiás
Resumo
The main purpose of this dissertation was to construct lower and upper bounds for the
cardinality of the error correcting codes for constant-weight, contained in the vector
space Fn
3 , where F3 is a field with three elements, knowing parameters such as length
and minimum distance code. We present the main results of linear algebra necessary to
develop the theory of codes and then the fundamental concepts of more practical class of
codes, the linear error correcting codes. We state the Totobola problem and the Football
problem, relating them to the theory of codes and present some bounds for the "covering
radius problem"for r = 1 , some values of n. In the last chapter, we conclude the work
with some examples that illustrate bounds of coverings for Fn
3 , with r = 2 and 3, and the
generalization of the problem, where we present the binary covering radius problem, the
case of multiple coverages and the extension of the idea, citing bounds for the cardinality
of the codes contained in the vector space over a finite field with any arbitrary number of
elements.
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RODRIGUES, Silvana da Silva. Bounds for Constant-Weight Codes. 2011. 52 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2011.