Double circulant LCD codes over Z 4

Minjia Shi (1) , Daitao Huang (1) , Lin Sok (2, 1) , Patrick Solé (3)

1 Anhui University [Hefei]
2 RUPP - Royal University of Phnom Penh
3 I2M - Institut de Mathématiques de Marseille

The codes in the title are studied with respect to existence, enumeration and asymptotic performance. Their Gray images are shown to satisfy a modified Gilbert-Varshamov bound. Explicit counting formulas are derived. Examples of modest lengths are given where Gray images of LCD Z(4)-codes outperform the best known binary linear LCD codes.

Mots clés: Z(4)-codes; Double circulant; Self-dual; LCD; Boolean; Masking

Domaines: Théorie des nombres [math.NT]; Théorie de l'information et codage [math.IT]

Minjia Shi, Daitao Huang, Lin Sok, Patrick Solé. Double circulant LCD codes over Z 4. Finite Fields and Their Applications, 2019, 58, pp.133-144. ⟨10.1016/j.ffa.2019.04.001⟩. ⟨hal-02178304⟩