Minimal linear codes derived from weakly regular bent and plateaued functions

Author:

Mesnager Sihem1ORCID,Sınak Ahmet2ORCID

Affiliation:

1. Department of Mathematics, University of Paris VIII 93526, Saint-Denis, LAGA, UMR 7539, CNRS, Sorbonne Paris Cité, University of Paris XIII 93430 Villetaneuse, Telecom Paris, 91120 Palaiseau, France

2. Department of Mathematics and Computer Science, Necmettin Erbakan University 42090 Konya, Turkey

Abstract

The construction of (minimal) linear codes from functions has received much attention in the literature. In this paper, we derive several minimal codes from the sets of pre-images of weakly regular plateaued and bent functions over the odd characteristic finite fields. Based on the recent construction method, we obtain six-weight and seven-weight minimal codes from these functions. The Hamming weights in proposed codes are calculated from the character sums of the sets based on the Walsh spectrum of the employed functions, while the weight distributions of the codes are determined from both the sizes of the employed sets and the Walsh distributions of the employed functions.

Funder

French Agence Nationale de la Recherche

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Algebra and Number Theory

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