Gray Images of Cyclic Codes over ℤ_p^2 and ℤ_pℤ_p^2

06/28/2022

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by   Minjia Shi, et al.

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In the paper, we firstly study the algebraic structures of ℤ_p ℤ_p^k-additive cyclic codes and give the generator polynomials and the minimal spanning set of these codes. Secondly, a necessary and sufficient condition for a class of ℤ_pℤ_p^2-additive codes whose Gray images are linear (not necessarily cyclic) over ℤ_p is given. Moreover, as for some special families of cyclic codes over ℤ_9 and ℤ_3 ℤ_9, the linearity of the Gray images is determined.