On the constructions of ZpZp2-linear generalized Hadamard codes.

Dipak K. Bhunia*, Cristina Fernández-Córdoba, Mercè Villanueva

*Autor corresponent d’aquest treball

Producció científica: Contribució a revistaArticleRecercaAvaluat per experts

7 Cites (Scopus)

Resum

The ZpZp2-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 Z2Z4-additive codes when p=2. A ZpZp2-linear generalized Hadamard (GH) code is a GH code over Zp which is the Gray map image of a ZpZp2-additive code. In this paper, we generalize some known results for ZpZp2-linear GH codes with p=2 to any p≥3 prime when α1≠0. First, we give a recursive construction of ZpZp2-additive GH codes of type (α12;t1,t2) with t1,t2≥1. We also present many different recursive constructions of ZpZp2-additive GH codes having the same type, and show that we obtain permutation equivalent codes after applying the Gray map. 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 ZpZp2-linear GH codes with α1≠0. Indeed, we observe that the constructed codes are not equivalent to the Zps-linear GH codes for any s≥2.

Idioma originalAnglès
Número d’article102093
Nombre de pàgines26
RevistaFinite Fields and Their Applications
Volum83
DOIs
Estat de la publicacióPublicada - d’oct. 2022

Fingerprint

Navegar pels temes de recerca de 'On the constructions of ZpZp2-linear generalized Hadamard codes.'. Junts formen un fingerprint únic.

Com citar-ho