A new family of p-ary self-orthogonal code from weakly regular plateaued functions

Linear codes with optimal parameters have a wide range of practical applications in fields such as cryptography, quantum theory and distributed storage. This paper generalizes the work of (Heng et al. Designs, Codes and Cryptography 91:3953-3976, 2023) to the general case utilizing weakly regular plateaued functions. To begin with, a new class of self-orthogonal codes is constructed by using weakly regular plateaued functions. Then, by using the properties of exponential sums tools over finite fields, we determine the related parameters as well as weight distributions of this codes. Moreover, the minimum distance of the dual of these augmented codes are shown to be 3. Finally, we study the constructed self-orthogonal codes and gain some new p-ary almost optimal or optimal LCD codes.