FIVE-WEIGHT CODES FROM THREE-VALUED CORRELATION OF M-SEQUENCES

Minjia Shi (1) , Liqin Qian (2) , Tor Helleseth (3) , Patrick Solé (4)

1 Anhui University [Hefei]
2 NUAA - Nanjing University of Aeronautics and Astronautics [Nanjing]
3 The Selmer Center in Secure Communication
4 I2M - Institut de Mathématiques de Marseille

In this paper, for each of six families of three-valued m-sequence correlation, we construct an infinite family of five-weight codes from trace codes over the ring R = F 2 + uF 2 , where u 2 = 0. The trace codes have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Their support structure is determined. An application to secret sharing schemes is given. The parameters of the binary image are [2 m+1 (2 m − 1), 4m, 2 m (2 m − 2 r)] for some explicit r.

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

Minjia Shi, Liqin Qian, Tor Helleseth, Patrick Solé. FIVE-WEIGHT CODES FROM THREE-VALUED CORRELATION OF M-SEQUENCES. Advances in Mathematics of Communications, 2021, ⟨10.3934/amc.2021022⟩. ⟨hal-03260352⟩