Determining the Number of One-Weight Cyclic Codes When Length and Dimension Are Given

  • Gerardo Vega
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)


We use techniques from linear recurring sequences, exponential sums and Gaussian sums, in order to present a set of characterizations for the one-weight irreducible cyclic codes over finite fields. Without using such techniques, a subset of these characterizations was already presented in [2]. By means of this new set of characterizations, we give an explicit expression for the number of one-weight cyclic codes, when the length and dimension are given.


One-weight cyclic codes linear recurring sequences exponential sums and Gaussian sums 


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  1. 1.
    Lidl, R., Niederreitter, H.: Finite Fields. Cambridge Univ. Press, Cambridge (1983)zbMATHGoogle Scholar
  2. 2.
    Vega, G., Wolfmann, J.: New Classes of 2-weight Cyclic Codes. Designs, Codes and Cryptography 42(3), 327–334 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Wolfmann, J.: Are 2-Weight Projective Cyclic Codes Irreducible? IEEE Trans. Inform. Theory. 51, 733–737 (2005)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Gerardo Vega
    • 1
  1. 1.Dirección General de Servicios de Cómputo Académico, Universidad Nacional Autónoma de México, 04510 México D.F.Mexico

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