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Designs, Codes and Cryptography

, Volume 41, Issue 1, pp 87–99 | Cite as

Pairs of codes with prescribed Hamming distances and coincidences

  • Vince GrolmuszEmail author
Article

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 ∈ {0,1,...,q − 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.

Keywords

Multi-linear polynomials Codes Hamming-distance Code-generation 

AMS Classification

94B60 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Computer ScienceEötvös UniversityBudapestHungary

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