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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.doi:10.4134/ckms.2011.26.3.427 fatcat:la37q7vtjnf25px4n5unixiv5u