Linear codes over finite rings are trace codes

Yaqi Lu (1) , Minjia Shi (1) , Marcus Greferath (2) , Patrick Solé (3)

1 Anhui University [Hefei]
2 UCD - University College Dublin [Dublin]
3 I2M - Institut de Mathématiques de Marseille

Linear codes over finite rings are described here as trace codes for a suitable generalization of the trace called a GF-trace. Cyclic codes over Galois rings are given a trace description as well. The main tools are the notion of trace dual bases, in the case of linear codes, and of normal bases of an extension ring over a ring, in the case of cyclic codes.

Mots clés: Finite ring; Linear codes; Cyclic codes; GF-trace; Trace representation; Basis

Domaines: Algèbre commutative [math.AC]

Yaqi Lu, Minjia Shi, Marcus Greferath, Patrick Solé. Linear codes over finite rings are trace codes. Discrete Mathematics, 2020, 343 (8), pp.111919. ⟨10.1016/j.disc.2020.111919⟩. ⟨hal-02539564⟩