Linear codes over finite rings are trace codes

Authors :: Minjia Shi
Yaqi Lu
Patrick Solé
Marcus Greferath
Anhui University [Hefei]
University College Dublin [Dublin] (UCD)
Institut de Mathématiques de Marseille (I2M)
Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
Source :: Discrete Mathematics, Discrete Mathematics, Elsevier, 2020, 343 (8), pp.111919. ⟨10.1016/j.disc.2020.111919⟩, Discrete Mathematics, 2020, 343 (8), pp.111919. ⟨10.1016/j.disc.2020.111919⟩
Publication Year :: 2020
Publisher :: HAL CCSD, 2020.
Abstract: International audience; 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.

Language :: English
ISSN :: 0012365X
Database :: OpenAIRE
Journal :: Discrete Mathematics, Discrete Mathematics, Elsevier, 2020, 343 (8), pp.111919. ⟨10.1016/j.disc.2020.111919⟩, Discrete Mathematics, 2020, 343 (8), pp.111919. ⟨10.1016/j.disc.2020.111919⟩
Accession number :: edsair.doi.dedup.....8b5cc2a3d1dc4e0c50d4f6747949ce13
Full Text :: https://doi.org/10.1016/j.disc.2020.111919⟩