Browse > Article
http://dx.doi.org/10.4134/CKMS.2011.26.3.427

IDEALS OF Zpn[X]/(Xl-1)  

Woo, Sung-Sik (Department of Mathematics Ewha Women's University)
Publication Information
Communications of the Korean Mathematical Society / v.26, no.3, 2011 , pp. 427-443 More about this Journal
Abstract
In [6, 8], we showed that any ideal of $\mathbb{Z}_4[X]/(X^l\;-\;1)$ is generated by at most two polynomials of the `standard' forms when l is even. The purpose of this paper is to find the `standard' generators of the cyclic codes over $\mathbb{Z}_{p^a}$ of length a multiple of p, namely the ideals of $\mathbb{Z}_{p^a}[X]/(X^l\;-\;1)$ with an integer l which is a multiple of p. We also find an explicit description of their duals in terms of the generators when a = 2.
Keywords
cyclic code over $\mathbb{Z}_{p^a}$; ideals of $\mathbb{Z}_{p^n}[X]/(X^l\-\1)$;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
Times Cited By SCOPUS : 0
연도 인용수 순위
1 S. S. Woo, Cyclic codes of length $2^n$ over $Z_4$, preprint, 2005.
2 S. S. Woo, Algebras with a nilpotent generator over $Z_{p^2}$ , Bull. Korean Math. Soc. 43 (2006), no. 3, 487-497.   과학기술학회마을   DOI   ScienceOn
3 M. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969.
4 N. Bourbaki, Elements of Mathematics. Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass., 1972.
5 S. T. Dougherty and Y. H. Park, On modular cyclic codes, Finite Fields Appl. 13 (2007), no. 1, 31-57.   DOI   ScienceOn
6 P. Kanwar and S. R. Lopez-Permouth, Cyclic codes over the integers modulo $p^m$, Finite Fields Appl. 3 (1997), no. 4, 334-352.   DOI   ScienceOn
7 R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge University Press, Cambridge, 1994.
8 S. S. Woo, Free cyclic codes over finite local rings, Bull. Korean Math. Soc. 43 (2006), no. 4, 723-735.   과학기술학회마을   DOI   ScienceOn
9 S. S. Woo, Cyclic codes of even length over $Z_4$, J. Korean Math. Soc. 44 (2007), no. 3, 697-706.   과학기술학회마을   DOI   ScienceOn