On self-dual and LCD double circulant and double negacirculant codes over $\mathbb{F}_q + u\mathbb{F}_q

Minjia Shi (1) , Hongwei Zhu , Liqin Qian , Lin Sok (1) , Patrick Solé (2)

1 Anhui University [Hefei]
2 I2M - Institut de Mathématiques de Marseille

Double circulant codes of length 2n over the semilocal ring R = F q + uF q , u 2 = u, are studied when q is an odd prime power, and −1 is a square in F q . Double negacircu- lant codes of length 2n are studied over R when n is even and q is an odd prime power. Exact enumeration of self-dual and LCD such codes for given length 2n is given. Em- ploying a duality-preserving Gray map, self-dual and LCD codes of length 4n over F q are constructed. Using random coding and the Artin conjecture, the relative distance of these codes is bounded below. The parameters of examples of the modest length are computed. Several such codes are optimal.

Domaines: Informatique [cs]

Minjia Shi, Hongwei Zhu, Liqin Qian, Lin Sok, Patrick Solé. On self-dual and LCD double circulant and double negacirculant codes over $\mathbb{F}_q + u\mathbb{F}_q. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences , 2020. ⟨hal-02488063⟩