JOURNAL BROWSE
Search
Advanced SearchSearch Tips
IDEALS OF Zpn[X]/(Xl-1)
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
IDEALS OF Zpn[X]/(Xl-1)
Woo, Sung-Sik;
  PDF(new window)
 Abstract
In [6, 8], we showed that any ideal of 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 of length a multiple of p, namely the ideals of 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 ;ideals of ;
 Language
English
 Cited by
1.
CYCLIC CODES OF LENGTH 2n OVER ℤ4,;

대한수학회논문집, 2013. vol.28. 1, pp.39-54 crossref(new window)
1.
CYCLIC CODES OF LENGTH 2nOVER ℤ4, Communications of the Korean Mathematical Society, 2013, 28, 1, 39  crossref(new windwow)
 References
1.
M. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969.

2.
N. Bourbaki, Elements of Mathematics. Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass., 1972.

3.
S. T. Dougherty and Y. H. Park, On modular cyclic codes, Finite Fields Appl. 13 (2007), no. 1, 31-57. crossref(new window)

4.
P. Kanwar and S. R. Lopez-Permouth, Cyclic codes over the integers modulo $p^m$, Finite Fields Appl. 3 (1997), no. 4, 334-352. crossref(new window)

5.
R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge University Press, Cambridge, 1994.

6.
S. S. Woo, Cyclic codes of even length over $Z_4$, J. Korean Math. Soc. 44 (2007), no. 3, 697-706. crossref(new window)

7.
S. S. Woo, Free cyclic codes over finite local rings, Bull. Korean Math. Soc. 43 (2006), no. 4, 723-735. crossref(new window)

8.
S. S. Woo, Cyclic codes of length $2^n$ over $Z_4$, preprint, 2005.

9.
S. S. Woo, Algebras with a nilpotent generator over $Z_{p^2}$ , Bull. Korean Math. Soc. 43 (2006), no. 3, 487-497. crossref(new window)