Additive complementary dual codes over F 4

Minjia Shi (1) , Na Liu (1) , Jon-Lark Kim (2) , Patrick Solé (3)

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

A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been a hot topic recently due to Boolean masking application in the security of embarked electronics (Carlet and Guilley, 2014). Additive codes over F 4 are F 4-codes that are stable by codeword addition but not necessarily by scalar multiplication. An additive code over F 4 is additive complementary dual (ACD) if it meets its dual trivially. The aim of this research is to study such codes which meet their dual trivially. All the techniques and problems used to study LCD codes are potentially relevant to ACD codes. Interesting constructions of ACD codes from binary codes are given with respect to the trace Hermitian and trace Euclidean inner product. The former product is relevant to quantum codes.

Mots clés: Additive code; finite field

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

Minjia Shi, Na Liu, Jon-Lark Kim, Patrick Solé. Additive complementary dual codes over F 4. Finite Fields and Their Applications, In press. ⟨hal-03789248⟩