2022/07/29 by Dipak K. Bhunia, Bhunia, Dipak Kumar, Cristina Fernández-Córdoba +3
Computer Science · Engineering · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2207.14702
openalex publication_date 2022/07/29 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
The ℤpℤp2…ℤps-additive codes are subgroups of ℤpα1 × ℤp2α2 × ⋯ × ℤpsαs, and can be seen as linear codes over ℤp when αi=0 for all i ∈ \2,…, s\, a ℤps-additive code when αi=0 for all i ∈ \1,…, s-1\ , or a ℤpℤp2-additive code when s=2, or ℤ2ℤ4-additive codes when p=2 and s=2. A ℤpℤp2…ℤps-linear generalized Hadamard (GH) code is a GH code over ℤp which is the Gray map image of a ℤpℤp2…ℤps-additive code. In this paper, we generalize some known results for ℤpℤp2…ℤps-linear GH codes with p prime and s≥ 2. First, we give a recursive construction of ℤpℤp2… ℤps-additive GH codes of type (α1,…,αs;t1,…,ts) with t1≥ 1, t2,…,ts-1≥ 0, and ts≥1. Then, we show for which types the corresponding ℤpℤp2…ℤps-linear GH codes are nonlinear over ℤp. We also compute the kernel and its dimension whenever they are nonlinear.