Parameterized codes over some embedded sets and their applications to complete graphs
Abstract
Let $K$ be a finite field, let $X \subset \mathbb{P}^{m-1}$ and $X' \subset \mathbb{P}^{r-1}$, 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 parameterized 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.
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.
Keywords
finite fields; regularity index; minimum distance; parameterized codes; embedded sets; complete graphs
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PDFISSN: 1331-0623 (Print), 1848-8013 (Online)