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Graph Theoretic Methods in Coding Theory

  • Salim El Rouayheb
  • Costas N. Georghiades
Chapter

Abstract

Let \({\Sigma }_{q} =\{ 0,1,\ldots,q - 1\}\) be an alphabet of order q. A q-ary (unrestricted) code C of length n and size | C | is a subset of Σ q n containing | C | elements called codewords. The Hamming weight wt(c) of a codeword c is the number of its nonzero entries. A constant-weight code is a code where all the codewords have the same Hamming weight. The Hamming distance d(c, c′) between two codewords c and c′ is the number of positions where they have different entries. The minimum Hamming distance of a code C is the largest integer Δ such that ∀c,c′C, d(c, c′) ≥ Δ.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.ECE DepartmentTexas A&M UniversityCollege StationUSA

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