The Weight Distribution of C_5(1, n)

  • Authors:

  • Kwok Yan Lam;Francesco Sica

  • Affiliations:

  • School of Computing, National University of Singapore, Lower Kent Ridge Road, Singapore 119260lamky@comp.nus.edu.sg;Universite Catholique, de Louvain, UCL Cryto Group, Place du levant 3, Louvain-la-neuve, Belgium B-1348sica@dice.ucl.ac.be

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2001

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Abstract

In [2] the codes C_q(r,n) over \Bbb{F}_q were introduced. These linear codes have parameters [2^n,\sum_{i=0}^r{{n}\choose i}, 2^{n-r}], can be viewed as analogues of the binary Reed-Muller codes and share several features in common with them. In [2], the weight distribution of C_3(1,n) is completely determined.In this paper we compute the weight distribution of C_5(1,n). To this end we transform a sum of a product of two binomial coefficients into an expression involving only exponentials an Lucas numbers. We prove an effective result on the set of Lucas numbers which are powers of two to arrive to the complete determination of the weight distribution of C_5(1,n). The final result is stated as Theorem 2.