CYCLIC CODES OF LENGTH 2n OVER ℤ4

Title & Authors
CYCLIC CODES OF LENGTH 2n OVER ℤ4
Woo, Sung Sik;

Abstract
The purpose of this paper is to find a description of the cyclic codes of length $\small{2^n}$ over $\small{\mathbb{Z}_4}$. We show that any ideal of $\small{\mathbb{Z}_4}$[X]/($\small{X^{2n}}$ - 1) is generated by at most two polynomials of the standard forms. We also find an explicit description of their duals in terms of the generators.
Keywords
cyclic code over $\small{\mathbb{Z}_4}$;
Language
English
Cited by
References
1.
M. F. Atiyah and I. G. Macdonald, Introduction to Commutative algebra, Addison-Wesley, 1969.

2.
S. T. Dougherty and Y. H. Park, On modular cyclic codes, Finite Fields Appl. 13 (2007), no. 1, 31-57.

3.
P. Kanwar and S. R. Lopez-Permouth, Cyclic codes over the integers modulo pm, Finite Fields Appl. 3 (1997), no. 4, 334-352.

4.
Bernard R. McDonald, Finite Rings with Identity, Marcel Dekker, 1974.

5.
S. S. Woo, Free cyclic codes over finite local rings, Bull. Korean Math. Soc. 43 (2006), no. 4, 723-735.

6.
S. S. Woo, Ideals of \${\mathbb{Z}}_p^n[X]/(X^l-1)\$, Commun. Korean Math. Soc. 26 (2011), no. 3, 427-443.

7.
S. S. Woo, Cyclic codes of even length over \${\mathbb{Z}}_4\$, J. Korean Math. Soc. 44 (2007), no. 3, 697-706.