The Weight Distribution of C5(1, n)

Kwok Yan Lam, Francesco Sica

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In [2] the codes Cq(r, n) over double-struck F signq were introduced. These linear codes have parameters [2n, ∑i=0 r (i n), 2n-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 C3(1, n) is completely determined. In this paper we compute the weight distribution of C5(1, n). To this end we transform a sum of a product of two binomial coefficients into an expression involving only exponentials and 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 C5(1, n). The final result is stated as Theorem 2.

Original languageEnglish
Pages (from-to)181-191
Number of pages11
JournalDesigns, Codes, and Cryptography
Volume24
Issue number2
DOIs
Publication statusPublished - Oct 2001
Externally publishedYes

Fingerprint

Weight Distribution
Lucas numbers
Reed-Muller Codes
Binomial coefficient
Binary Code
Linear Codes
Transform
Analogue
Theorem

Keywords

  • Lucas numbers
  • Weight distribution

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

The Weight Distribution of C5(1, n). / Lam, Kwok Yan; Sica, Francesco.

In: Designs, Codes, and Cryptography, Vol. 24, No. 2, 10.2001, p. 181-191.

Research output: Contribution to journalArticle

Lam, Kwok Yan ; Sica, Francesco. / The Weight Distribution of C5(1, n). In: Designs, Codes, and Cryptography. 2001 ; Vol. 24, No. 2. pp. 181-191.
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