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Article Dans Une Revue On Number Theory and its Applications Année : 2008

On the semiprimitivity of cyclic codes

Résumé

We prove, without assuming the Generalized Riemann Hypothesis, but with at most one exception, that an irreducible cyclic code c(p,m,v) with v prime and p of index 2 modulo v is a two-weight code if and only if it is a semiprimitive code or it is one of the six sporadic known codes. The result is proved without any exception for index-two irreducible cyclic c(p,m,v) codes with v prime not congruent to 3 modulo 8. Finally, we prove that these two results hold true in fact for irreducible cyclic code c(p,m,v) such that there is three p-cyclotomic cosets modulo v.
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Dates et versions

hal-00978910 , version 1 (14-04-2014)

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Yves Aubry, Philippe Langevin. On the semiprimitivity of cyclic codes. On Number Theory and its Applications, 2008, 5, pp.284--293. ⟨10.1142/6761⟩. ⟨hal-00978910⟩
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