A first step towards the skew duadic codes

International audienceThis text gives a first definition of the $\theta$-duadic codes where $\theta$ is an automorphism of $F q$. A link with the weakly self-dual $\theta$-cyclic codes is established. A construction and an enumeration are provided when $q$ is the square of a prime number $p$. In addition, new self-dual binary codes $ [72, 36, 12] $ are obtained from extended $\theta$-duadic codes defined on $F 4$