Further designs for self-orthogonal and LCD codes developed from functions over finite fields

Abstract The construction of linear codes from functions in finite fields has been widely studied in the literature. There are two generic construction methods: the first and second generic construction methods for generating linear codes from functions over finite fields. In this paper, we first define the augmented code construction of the variation of the second generic construction method and then present new infinite families of four- and five-weight self-orthogonal divisible codes derived from trace functions. Moreover, by using the augmented code construction based on the first generic construction method, we construct new infinite families of three-weight and four-weight self-orthogonal divisible codes from weakly regular plateaued functions. We determine all parameters of the constructed self-orthogonal codes as well as their dual codes over the odd characteristic finite fields. We present Hamming weights and their weight distributions for the constructed self-orthogonal codes. Additionally, we utilise the constructed $$ p $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -ary self-orthogonal codes to develop $$ p $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -ary Linear Complementary Dual (LCD) codes and determine the parameters of the obtained LCD codes and their dual codes.