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Article Dans Une Revue Discrete Mathematics Année : 2020

Asymptotic performance of metacyclic codes

Résumé

A finite group with a cyclic normal subgroup N such that G/N is cyclic is said to be metacyclic. A code over a finite field F is a metacyclic code if it is a left ideal in the group algebra FG for G a metacyclic group. Metacyclic codes are generalizations of dihedral codes, and can be constructed as quasi-cyclic codes with an extra automorphism. In this paper, we prove that metacyclic codes form an asymptotically good family of codes. Our proof relies on a version of Artin's conjecture for primitive roots in arithmetic progression being true under the Generalized Riemann Hypothesis (GRH).
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Dates et versions

hal-02523289 , version 1 (28-03-2020)

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  • HAL Id : hal-02523289 , version 1

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Martino Borello, Pieter Moree, Patrick Solé. Asymptotic performance of metacyclic codes. Discrete Mathematics, 2020, 343 (7), pp.111885. ⟨hal-02523289⟩
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