ā„¤_pā„¤_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 = Ī¦(š’ž) is called ā„¤_p ā„¤_p^2-linear if it's the Gray image of the ā„¤_p ā„¤_p^2-additive code š’ž. In this paper, the rank and the dimension of the kernel of š’ž are studied. Both of the codes āŸØĪ¦(š’ž) āŸ© and (Ī¦(š’ž)) are proven ā„¤_p ā„¤_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 ā„¤_p ā„¤_p^2-additive cyclic codes are considered.

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