Title:

Exploring invariant linear codes through generators and centralizers (English) 
Author:

Dey, Partha Pratim 
Language:

English 
Journal:

Archivum Mathematicum 
ISSN:

00448753 (print) 
ISSN:

12125059 (online) 
Volume:

41 
Issue:

1 
Year:

2005 
Pages:

1726 
Summary lang:

English 
. 
Category:

math 
. 
Summary:

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. (English) 
Keyword:

invariant code 
Keyword:

centralizer 
Keyword:

affine plane 
MSC:

05E20 
MSC:

94B05 
idZBL:

Zbl 1115.05097 
idMR:

MR2142140 
. 
Date available:

20080606T22:45:00Z 
Last updated:

20120510 
Stable URL:

http://hdl.handle.net/10338.dmlcz/107932 
. 
Reference:

[1] Hall M.: Combinatorial Theory.New YorkChichesterBrisbaneToronto Singapore: Interscience (1986). Zbl 0588.05001, MR 0840216 
Reference:

[2] Hughes D. R., Piper F. C.: Projective Planes.BerlinHeidelberg New York: Springer Verlag (1973). Zbl 0267.50018, MR 0333959 
. 