Rank and pairs of Rank and Dimension of Kernel of ℤ_pℤ_p²-linear codes

2022/07/26 by Xiaoxiao Li, Li, Xiaoxiao, Minjia Shi +3
Computer Science · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2207.12613

openalex publication_date 2022/07/26 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

A code C is called ℤ_pℤ_p²-linear if it is the Gray image of a ℤ_pℤ_p²-additive code. For any prime number p larger than 3, the bounds of the rank of ℤ_pℤ_p²-linear codes are given. For each value of the rank and the pairs of rank and the dimension of the kernel of ℤ_pℤ_p²-linear codes, we give detailed construction of the corresponding codes. Finally, as an example, the rank and the dimension of the kernel of ℤ₅ℤ₂₅-linear codes are studied.

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