 |
Title |
 |
|
Free cyclic codes over finite local rings(ENG) |
|
|
Author |
|
|
Sung Sik Woo |
|
|
MSC |
|
|
13C10 |
|
|
Publication |
|
|
|
|
|
Page |
|
|
723-735 Page |
|
|
Abstract |
|
|
1. Introduction
2. Polynomials over finite rings
3. Free cyclic codes of length $m$ over $Bbb Z_{p^k}$ with $(m,p)=1$
4. Free cyclic codes of length $n$ over $Bbb Z_{p^k}$ with $(n,p)
ot=1$
5. Cyclic codes of length $n$ over finite local rings
6. Duality of free cyclic codes |
|
|
Own Status |
|
|
|
|
|
Keyword |
|
|
free modules over a finite commutative rings, separable extension of local rings, cyclic codes over $Bbb Z_{p^k}$ |
|
|
Note |
|
|
|
|
|
Summary |
|
|
In [2] it was shown that a
1-generator quasi-cyclic code $C$ of length $n=ml$ of index $l$
over $Bbb Z_4$ is free if $C$ is generated by a polynomial which
divides $X^m-1$. In this paper, we prove that a necessary and
sufficient condition for a cyclic code over $Bbb Z_{p^k}$ of
length $m$ to be free is that it is generated by a polynomial
which divides $X^m-1$. We also show that this can be extended to
finite local rings with a principal maximal ideal. |
|
|
Attach |
|
|
[DVI] [PDF] |
|