ℤ_pℤ_p^2-linear codes: rank and kernel

05/27/2022

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by   Minjia Shi, et al.

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A code C is called _p_p^2-linear if it is the Gray image of a _p_p^2-additive code, where p>2 is prime. In this paper, the rank and the dimension of the kernel of _p_p^2-linear codes are studied. Two bounds of the rank of a _3_9-linear code and the dimension of the kernel of a _p_p^2-linear code are given, respectively. For each value of these bounds, we give detailed construction of the corresponding code. Finally, pairs of rank and the dimension of the kernel of _3_9-linear codes are also considered.