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http://dx.doi.org/10.4134/BKMS.2006.43.4.723

FREE CYCLIC CODES OVER FINITE LOCAL RINGS  

Woo, Sung-Sik (DEPARTMENT OF MATHEMATICS, EWHA WOMEN'S UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.4, 2006 , pp. 723-735 More about this Journal
Abstract
In [2] it was shown that a 1-generator quasi-cyclic code C of length n = ml of index l over $\mathbb{Z}_4$ 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 $\mathbb{Z}_pk$ 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.
Keywords
free modules over a finite commutative rings; separable extension of local rings; cyclic codes over $\mathbb{Z}_pk$;
Citations & Related Records

Times Cited By SCOPUS : 3
연도 인용수 순위
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