Several new classes of p-ary weakly regular plateaued functions and minimal codes with several weights

Plateaued functions, including bent functions, are crucial in cryptography due to their possession of a range of desirable cryptographic properties. Weakly regular plateaued functions can also be employed in many domains. In particular, they have been widely used in designing good linear codes for several applications (such as secret sharing and two-party computation), association schemes, and strongly regular graphs. This paper is devoted to weakly regular plateaued functions, whose objectives are twofold. First, we aim to generate new infinite families of weakly regular plateaued functions and then, to design new families of p-ary linear codes and investigate their use for some standard applications after studying its minimality based on their weight distributions. More specifically, we present several classes of weakly regular plateaued functions from monomial bent functions, and determine their corresponding dual functions explicitly. Furthermore, we exploit our constructions to derive several new classes of minimal linear codes violating the Ashikhmin-Barg condition with six, seven, nine, ten or eleven weights, which are more appropriate for several applications.