Graph Theoretic Methods in Coding Theory - Texas A&M University (TAMU) Scholar

© Springer Science+Business Media, LLC 2012. All rights reserved. Let Σ q ={0,1,…, q?1} be an alphabet of order q. A q-ary (unrestricted) code C of length n and size | C | is a subset of Σqn 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, d(c, c?) ≥ Δ.

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