Constant Weight Codes and Group Divisible Designs

Authors:
Simon Blake-Wilson;Kevin T. Phelps
Affiliations:
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom.;Department of Discrete and Statistical Sciences, Auburn University, Auburn, AL 36849-5307, U.S.A.
Venue:
Designs, Codes and Cryptography
Year:
1999

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Abstract

The studyof a class of optimal constant weight codes over arbitrary alphabetswas initiated by Etzion, who showed that such codes are equivalentto special GDDs known as generalized Steiner systems GS(t,k,n,g)Etzion. This paper presents new constructions for these systemsin the case t=2, k=3. In particular,these constructions imply that the obvious necessary conditionson the length n of the code for the existence ofan optimal weight 3, distance 3 code over an alphabet of arbitrarysize are asymptotically sufficient.