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Multi-twisted codes as free modules over principal ideal domains
[article]
2022
arXiv
pre-print
We begin this chapter by introducing the simple algebraic structure of cyclic codes over finite fields. This structure undergoes a series of generalizations to present algebraic descriptions of constacyclic, quasi-cyclic (QC), quasi-twisted (QT), generalized quasi-cyclic (GQC), and multi-twisted (MT) codes. The correspondence between these codes and submodules of the free 𝔽_q[x]-module (𝔽_q[x])^ℓ is established. Thus, any of these codes corresponds to a free linear code over the principal ideal
arXiv:2204.03156v1
fatcat:jsa3r2kmjzf6jklwjuod3bkdxm