Z 2 Z 4 -Additive Quasi-Cyclic codes

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

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

We study the codes of the title by the CRT method, that decomposes such codes into constituent codes, which are shorter codes over larger alphabets. Criteria on these constituent codes for self-duality and linear complementary duality of the decomposed codes are derived. The special class of the one-generator codes is given a polynomial representation and exactly enumerated. In particular, we present some illustrative examples of binary linear codes derived from the Z2Z4-additive quasi-cyclic codes that meet the Griesmer bound with equality.

Mots clés: Z2Z4-additive quasi-cyclic codes; Chinese Remainder Theorem; self-dual codes; ACD codes

Domaines: Théorie de l'information [cs.IT]

Minjia Shi, Shitao Li, Patrick Solé. Z 2 Z 4 -Additive Quasi-Cyclic codes. IEEE Transactions on Information Theory, 2021. ⟨hal-03334758⟩