On Z_pZ_p^k-additive codes and their duality

08/31/2018

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by   Minjia Shi, et al.

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In this paper, two different Gray like maps from Z_p^a × Z_p^k^b to Z_p^n, n=a+p^k-1b, denoted by ϕ and Φ, respectively, are presented, where p is a prime number. We have determined the connection between the weight enumerators among the image codes under these two mappings. We show that if C is a Z_pZ_p^k-additive code, and C^ is its dual, then the weight enumerators of the image p-ary codes ϕ(C) and Φ(C^) are formally dual. This is a partial generalization of results in [On Z_2^k-dual binary codes, arXiv:math/0509325]. Additionally, a construction of 1-perfect additive codes in the mixed Z_p Z_p^2 ... Z_p^k alphabet