Parameterized codes over some embedded sets and their applications to complete graphs

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Resumen

Let K be a finite field, let X ⊂ ℙm-1 and X′ ⊂ ℙr-1, with r < m, be two algebraic toric sets parameterized by some monomials in such a way that X′ is embedded in X. We describe the relations among the main parameters of the corresponding parameter-ized linear codes of order d associated to X and X′ by using some tools from commutative algebra and algebraic geometry. We also find the regularity index in the case of toric sets parameterized by the edges of a complete graph. Finally, we give some bounds for the minimum distance of the linear codes associated to complete graphs.

Idioma originalInglés
Páginas (desde-hasta)377-391
Número de páginas15
PublicaciónMathematical Communications
Volumen18
N.º2
EstadoPublicada - 2013

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