# IDEALS OF Zpn[X]/(Xl-1)

• Woo, Sung-Sik (Department of Mathematics Ewha Women's University)
• Received : 2010.04.06
• Published : 2011.07.31
• 68 12

#### 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 $\mathbb{Z}_{p^n}[X]/(X^l\-\1)$

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#### Cited by

1. CYCLIC CODES OF LENGTH 2nOVER ℤ4 vol.28, pp.1, 2013, https://doi.org/10.4134/CKMS.2013.28.1.039