Ideals of Z_(p^n)[X]/((X^l)-1)
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In [6, 8], we showed that any ideal of 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 Z_(p^a) of length a multiple of p, namely the ideals of 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.
Abstract
In [6, 8], we showed that any ideal of 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 Z_(p^a) of length a multiple of p, namely the ideals of 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.
참고문헌 (9)
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