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On Cosets of Weight 4 of Binary BCH Codes with Minimum Distance 8 and Exponential Sums

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Abstract

We study coset weight distributions of binary primitive (narrow-sense) BCH codes of length n = 2m (m odd) with minimum distance 8. In the previous paper [1], we described coset weight distributions of such codes for cosets of weight j = 1, 2, 3, 5, 6. Here we obtain exact expressions for the number of codewords of weight 4 in terms of exponential sums of three types, in particular, cubic sums and Kloosterman sums. This allows us to find the coset distribution of binary primitive (narrow-sense) BCH codes with minimum distance 8 and also to obtain some new results on Kloosterman sums over finite fields of characteristic 2.

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Authors and Affiliations

  1. Institute for Information Transmission Problems, RAS, Moscow, Russia

    V. A. Zinoviev

  2. Department of Informatics, University of Bergen, Norway

    T. Helleseth

  3. INRIA, Domaine de Voluceau-Rocquencourt, France

    P. Charpin

Authors
  1. V. A. Zinoviev
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  2. T. Helleseth
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  3. P. Charpin
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__________

Translated from Problemy Peredachi Informatsii, No. 4, 2005, pp. 36–56.

Original Russian Text Copyright © 2005 by Zinoviev, Helleseth, Charpin.

Supported by INRIA-Rocquencourt, France, the Norwegian Research Council, Grant no. 146874/420, and the Russian Foundation for Basic Research, project no. 03-01-00098.

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Zinoviev, V.A., Helleseth, T. & Charpin, P. On Cosets of Weight 4 of Binary BCH Codes with Minimum Distance 8 and Exponential Sums. Probl Inf Transm 41, 331–348 (2005). https://doi.org/10.1007/s11122-006-0003-4

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  • DOI: https://doi.org/10.1007/s11122-006-0003-4

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