Construction of isodual codes from polycirculant matrices

Minjia Shi (1) , Li Xu (1) , Patrick Solé (2)

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

Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can only occur over F 2 in the double circulant case. Building on an explicit infinite sequence of irreducible trinomials over F 2 , we show that binary double polycirculant codes are asymptotically good.

Domaines: Mathématiques [math]

Minjia Shi, Li Xu, Patrick Solé. Construction of isodual codes from polycirculant matrices. Designs, Codes and Cryptography, 2020, ⟨10.1007/s10623-020-00799-8⟩. ⟨hal-02944227⟩