Polycyclic codes as invariant subspaces.

Minjia Shi (1) , Xiaoxiao Li (1) , Zahra Sepasdar (2) , Patrick Solé (3)

1 School of Mathematical Sciences [Anhui]
2 Shiraz University - Shiraz University
3 I2M - Institut de Mathématiques de Marseille

Polycyclic codes are a powerful generalization of cyclic and constacyclic codes. Their algebraic structure is studied here by the theory of invariant subspaces from linear algebra. As an application, a bound on the minimum distance of these codes is derived which outperforms, in some cases, the natural analogue of the BCH bound.

Mots clés: Polycyclic codes; cyclic codes; BCH bound; invariant subspaces

Domaines: Mathématiques [math]

Minjia Shi, Xiaoxiao Li, Zahra Sepasdar, Patrick Solé. Polycyclic codes as invariant subspaces.. Finite Fields and Their Applications, 2020, ⟨10.1016/j.ffa.2020.101760⟩. ⟨hal-02945186⟩