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

Özet

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 these codes from special functions over the odd characteristic 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 five different subsets of the preimages of weakly regular plateaued balanced functions. We then obtain five infinite classes of minimal linear codes with six-weights based on these functions over the odd characteristic finite fields.