Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2013; 28(1): 39-54

Printed January 31, 2013

https://doi.org/10.4134/CKMS.2013.28.1.39

Copyright © The Korean Mathematical Society.

Cyclic codes of length $2^n$ over $\Bbb Z_4$

Sung Sik Woo

Ewha Women's University

Abstract

The purpose of this paper is to find a description of the cyclic codes of length $2^n$ over $\Bbb Z_4$. We show that any ideal of $\Bbb Z_4[X]/(X^{2^n}-1)$ 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 $\Bbb Z_4$

MSC numbers: 94B15

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