Dual transform and projective self-dual codes
Iliya Bouyukliev, Stefka Bouyuklieva · Advances in Mathematics of Communications · 2023
We present and analyze the relation between different types of linear codes through the (projective) dual transform. The considered codes are represented by a generator matrix or a characteristic vector, and the dual transform is defined in these terms. This allows us to extend its use to study codes with special properties, which we call self-polar, and their relation to Boolean functions. The self-polar codes are a special class of projective self-dual codes and are closely connected with self-dual and anti-self-dual bent functions. We also give some computational results for self-dual bent functions in eight variables.