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

Title & Authors
IDEALS OF Zpn[X]/(Xl-1)
Woo, Sung-Sik;

Abstract
In [6, 8], we showed that any ideal of $\small{\mathbb{Z}_4[X]/(X^l\;-\;1)}$ 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 $\small{\mathbb{Z}_{p^a}}$ of length a multiple of p, namely the ideals of $\small{\mathbb{Z}_{p^a}[X]/(X^l\;-\;1)}$ 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 $\small{\mathbb{Z}_{p^a}}$;ideals of $\small{\mathbb{Z}_{p^n}[X]/(X^l\-\1)}$;
Language
English
Cited by
1.
CYCLIC CODES OF LENGTH 2n OVER ℤ4,;

대한수학회논문집, 2013. vol.28. 1, pp.39-54
1.
CYCLIC CODES OF LENGTH 2nOVER ℤ4, Communications of the Korean Mathematical Society, 2013, 28, 1, 39
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