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Linear codes with balanced weight distribution

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Abstract

In this paper, we study particular linear codes defined overF q , with an astonishing property, their weight distribution is balanced, i.e. there is the same number of codewords for each nonzero weight of the code. We call these codesBWD-codes. We first study BWD-codes by means of the Pless identities and we completely characterize the two-weight projective case. We study the class of codes defined under subgroups of the multiplicative group ofF q s, using the Gauss sums. Then, given a primep and an integerN dividingp − 1, we construct all theN-weight BWD-codes of that class. We conclude this paper by some tables of BWD-codes and an open problem.

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Authors and Affiliations

  1. G.E.C.T., Université de Toulon et du Var, B.P. 132, F-83957, La Garde Cedex, France

    P. Langevin & J. P. Zanotti

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  1. P. Langevin
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  2. J. P. Zanotti
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Langevin, P., Zanotti, J.P. Linear codes with balanced weight distribution. AAECC 6, 299–307 (1995). https://doi.org/10.1007/BF01235721

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  • DOI: https://doi.org/10.1007/BF01235721

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