In this talk, we will present enumeration algorithms of skew cyclic codes for a finite field extension when the characteristic is odd and coprime to the code length over the degree of the extension, that is, in the separable case.

In a first part of the talk, we will define an explicit bijection between selfdual skew cyclic codes and families of totally maximal isotropic subspaces in some Euclidean or Hermitian spaces.

In a second part, we will use this bijection together with classical counting results in finite geometry to count selfdual skew cyclic codes, generate them randomly according to the uniform distribution and enumerate them.

To conclude, we will illustrate these methods by factorizing selfdual skew cyclic code generators in the purely inseparable case, into separable ones, providing thus an exhaustive though redundant enumeration algorithm in the general case. Finally, we will report on an implementation of our enumeration algorithms in SageMath, and provide some numerical results.

This is a joint work with Xavier Caruso.