Pairs of codes with prescribed Hamming distances and coincidences

Authors:
Vince Grolmusz
Affiliations:
Department of Computer Science, Eötvös University, Budapest, Hungary H-1117
Venue:
Designs, Codes and Cryptography
Year:
2006

Citing 6
Cited 0

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Note: on k-wise set-intersections and k-wise Hamming-distances

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Constructing set systems with prescribed intersection sizes

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Abstract

The main problem of coding theory is to construct codes with large Hamming-distances between the code-words. In this work we describe a fast algorithm for generating pairs of q-ary codes with prescribed pairwise Hamming-distances and coincidences (for a letter s 驴 {0,1,...,q 驴 1}, the number of s-coincidences between codewords a and b is the number of letters s in the same positions both in a and b). The method is a generalization of a method for constructing set-systems with prescribed intersection sizes (Grolmusz (2002) Constructing set-systems with prescribed intersection sizes. J Algorithms 44:321---337), where only the case q = 2 and s = 1 was examined. As an application, we show that the modular version of the classical Delsarte-inequality does not hold for odd, non-prime power composite moduli.