Exploring invariant linear codes through generators and centralizers

Dey, Partha Pratim. "Exploring invariant linear codes through generators and centralizers." Archivum Mathematicum 041.1 (2005): 17-26. <http://eudml.org/doc/249497>.

@article{Dey2005,
abstract = {We investigate a $H$-invariant linear code $C$ over the finite field $F_\{p\}$ where $H$ is a group of linear transformations. We show that if $H$ is a noncyclic abelian group and $(\vert \{H\}\vert ,p)=1$, then the code $C$ is the sum of the centralizer codes $C_\{c\}(h)$ where $h$ is a nonidentity element of $H$. Moreover if $A$ is subgroup of $H$ such that $A\cong Z_\{q\} \times Z_\{q\}$, $q\ne p$, then dim $C$ is known when the dimension of $C_\{c\}(K)$ is known for each subgroup $K\ne 1$ of $A$. In the last few sections we restrict our scope of investigation to a special class of invariant codes, namely affine codes and their centralizers. New results concerning the dimensions of these codes and their centralizers are obtained.},
author = {Dey, Partha Pratim},
journal = {Archivum Mathematicum},
keywords = {invariant code; centralizer; affine plane; affine plane},
language = {eng},
number = {1},
pages = {17-26},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Exploring invariant linear codes through generators and centralizers},
url = {http://eudml.org/doc/249497},
volume = {041},
year = {2005},
}

TY - JOUR
AU - Dey, Partha Pratim
TI - Exploring invariant linear codes through generators and centralizers
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 1
SP - 17
EP - 26
AB - We investigate a $H$-invariant linear code $C$ over the finite field $F_{p}$ where $H$ is a group of linear transformations. We show that if $H$ is a noncyclic abelian group and $(\vert {H}\vert ,p)=1$, then the code $C$ is the sum of the centralizer codes $C_{c}(h)$ where $h$ is a nonidentity element of $H$. Moreover if $A$ is subgroup of $H$ such that $A\cong Z_{q} \times Z_{q}$, $q\ne p$, then dim $C$ is known when the dimension of $C_{c}(K)$ is known for each subgroup $K\ne 1$ of $A$. In the last few sections we restrict our scope of investigation to a special class of invariant codes, namely affine codes and their centralizers. New results concerning the dimensions of these codes and their centralizers are obtained.
LA - eng
KW - invariant code; centralizer; affine plane; affine plane
UR - http://eudml.org/doc/249497
ER -