<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we will compute the main parameters of the parameterized codes arising from cycles. In the case of odd cycles the corresponding codes are the evaluation codes associated to the projective torus and the results are well known. In the case of even cycles we will compute the length and the dimension of the corresponding codes and also we will find lower and upper bounds for the minimum distance of this kind of codes. In many cases our upper bound is sharper than the Singleton bound.</p></abstract>

In this paper we will compute the main parameters of the parameterized codes arising from cycles. In the case of odd cycles the corresponding codes are the evaluation codes associated to the projective torus and the results are well known. In the case of even cycles we will compute the length and the dimension of the corresponding codes and also we will find lower and upper bounds for the minimum distance of this kind of codes. In many cases our upper bound is sharper than the Singleton bound.

Parameterized Codes over Cycles

Departamento de Ciencias Basicas, Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologias Avanzadas, Instituto Politecnico Nacional, 07340, Mexico, D.F. Partially supported by COFAA-IPN and SNI

Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, Instituto Politáecnico Nacional, 07300, Máexico, D.F. Partially supported by CONACyT

Departamento de Matemáticas, Escuela Superior de Física y Matematicas, Ínstituto Politecnico Nacional, 07300, Mexico, D.F. Partially supported by COFAA-ÍPN and SNÍ

Departamento de Matemaáticas, Escuela Superior de Física y Matematicas, Instituto Politáecnico Nacional, 07300, Mexico, D.F. Partially supported by SNI

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Parameterized Codes over Cycles"}

In this paper we will compute the main parameters of the parameterized codes arising from cycles. In the case of odd cycles the corresponding codes are the...

Parameterized Codes over Cycles

Published Online: Mar 05, 2014

Page range: 241 - 256

DOI: https://doi.org/10.2478/auom-2013-0056

Keywords
Cycle, Parameterized code, Minimum distance

This content is open access.

Parameterized Codes over Cycles

Published Online: Mar 05, 2014

Page range: 241 - 256

DOI: https://doi.org/10.2478/auom-2013-0056

KeywordsCycle, Parameterized code, Minimum distance

This content is open access.

Keywords
Cycle, Parameterized code, Minimum distance