2022/03/29 by Bhunia, Dipak K., Fernández-Córdoba, Cristina, Villanueva, Mercè
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2203.15657
The \Zp\Zp2-additive codes are subgroups of \Zpα1 × \Zp2α2, and can be seen as linear codes over \Zp when α2=0, \Zp2-additive codes when α1=0, or \Z2\Z4-additive codes when p=2. A \Zp\Zp2-linear generalized Hadamard (GH) code is a GH code over \Zp which is the Gray map image of a \Zp\Zp2-additive code. In this paper, we generalize some known results for \Zp\Zp2-linear GH codes with p=2 to any p≥ 3 prime when α1 ≠ 0. First, we give a recursive construction of \Zp\Zp2-additive GH codes of type (α1,α2;t1,t2) with t1,t2≥ 1. Then, we show for which types the corresponding \Zp\Zp2-linear GH codes are non-linear over \Zp. Finally, according to some computational results, we see that, unlike \Z4-linear GH codes, when p≥ 3 prime, the \Zp2-linear GH codes are not included in the family of \Zp\Zp2-linear GH codes with α1\not =0.