Infinite Classes of Six-Weight Linear Codes Derived from Weakly Regular Plateaued Functions

Abstract

The construction of (minimal) linear codes has received much attention, especially from cryptographic functions owing to the desirable properties of these functions. One application of minimal codes is the design of secret sharing schemes, which is a vital research topic of cryptography and has widely used in information protection. In the present paper, to propose new minimal linear codes we generalize the very recent construction method presented by Xu, Qu, and Luo at the international conference SETA-2020 for weakly regular plateaued unbalanced functions over odd characteristic finite fields. We derive six-weight minimal linear codes from the set of pre-image of these functions. We also construct two new infinite classes of six-weight minimal linear codes from weakly regular bent and plateaued unbalanced functions by proposing two different subsets of the pre-image of these functions.