| Title:
|
Exploring invariant linear codes through generators and centralizers (English) |
| Author:
|
Dey, Partha Pratim |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
17-26 |
| 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:
|
2008-06-06T22:45:00Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107932 |
| . |
| Reference:
|
[1] Hall M.: Combinatorial Theory.New York-Chichester-Brisbane-Toronto- Singapore: Interscience (1986). Zbl 0588.05001, MR 0840216 |
| Reference:
|
[2] Hughes D. R., Piper F. C.: Projective Planes.Berlin-Heidelberg- New York: Springer Verlag (1973). Zbl 0267.50018, MR 0333959 |
| . |
