Rank and pairs of Rank and Dimension of Kernel of ℤ_pℤ_p^2-linear codes

07/26/2022

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by   Xiaoxiao Li, et al.

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A code C is called ℤ_pℤ_p^2-linear if it is the Gray image of a ℤ_pℤ_p^2-additive code. For any prime number p larger than 3, the bounds of the rank of ℤ_pℤ_p^2-linear codes are given. For each value of the rank and the pairs of rank and the dimension of the kernel of ℤ_pℤ_p^2-linear codes, we give detailed construction of the corresponding codes. Finally, as an example, the rank and the dimension of the kernel of ℤ_5ℤ_25-linear codes are studied.