• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.697-706
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• 2007

In [8], we showed that any ideal of $\mathbb{Z}_4[X]/(X^{2^n}-1)$ is generated by at most two polynomials of the standard forms. The purpose of this paper is to find a description of the cyclic codes of even length over $\mathbb{Z}_4$ namely the ideals of $\mathbb{Z}_4[X]/(X^l\;-\;1)$, where $l$ is an even integer.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.427-443
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• 2011

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.