ℤ_pℤ_p^2-additive cyclic codes: kernel and rank

06/28/2022

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by   Xuan Wang, et al.

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A code C = Φ(𝒞) is called ℤ_p ℤ_p^2-linear if it's the Gray image of the ℤ_p ℤ_p^2-additive code 𝒞. In this paper, the rank and the dimension of the kernel of 𝒞 are studied. Both of the codes ⟨Φ(𝒞) ⟩ and (Φ(𝒞)) are proven ℤ_p ℤ_p^2-additive cyclic codes, and their generator polynomials are determined. Finally, accurate values of rank and the dimension of the kernel of some classes of ℤ_p ℤ_p^2-additive cyclic codes are considered.