Minimal linear codes with six-weights based on weakly regular plateaued balanced functions

Year 2021, Volume: 10 Issue: 3, 86 - 98, 01.09.2021

Ahmet Sınak

Abstract

Constructing minimal linear codes has a great interest in coding theory since they have an important role in describing access structures in secret sharing schemes and they are employed to design secure two-party computation protocols. Many methods of constructing linear codes have been proposed in the literature, and the most famous one is based on functions over finite fields. Linear codes derived from cryptographic functions have desirable algebraic structures that are significant from the application point of view. We in this paper study the construction of linear codes from some cryptographic functions over finite fields. We aim to construct new minimal codes by using a new type of function in the known construction method. To do this, we propose to use new subsets of the pre-images of weakly regular plateaued balanced functions. We then obtain five infinite classes of six-weight minimal codes from five different subsets of the pre-images of these functions.

Keywords

Balanced function, minimal code, weakly regular plateaued function, weight distribution

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