Trace codes over Z 4 , and Boolean functions

Minjia Shi (1) , Yan Liu (1) , Hugues Randriambololona (2) , Lin Sok (1) , Patrick Sole (3)

1 Anhui University [Hefei]
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 LAGA - Laboratoire Analyse, Géométrie et Applications

We construct trace codes over Z 4 based on Boolean functions and their support. The Lee weight distribution of these codes is studied by using the Walsh-Hadamard transform of the Boolean functions, and exponential character sums. We obtain few weights codes. In particular, bent and semi-bent functions give three-weight codes.

Domaines: Cryptographie et sécurité [cs.CR]

Minjia Shi, Yan Liu, Hugues Randriambololona, Lin Sok, Patrick Sole. Trace codes over Z 4 , and Boolean functions. Designs, Codes and Cryptography, 2019, 87, pp.1447 - 1455. ⟨10.1007/s10623-018-0542-x⟩. ⟨hal-02411617⟩