Codes associated with triangular graphs and permutation decoding

Authors:
J. D. Key;J. Moori;B. G. Rodrigues
Affiliations:
School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg 3209, South Africa.;School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg 3209, South Africa.;School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041, South Africa
Venue:
International Journal of Information and Coding Theory
Year:
2010

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Abstract

Linear codes that can be obtained from designs associated with the complete graph on n vertices and its line graph, the triangular graph, are examined. The codes have length n choose 2, dimension n or n − 1, and minimum weight n − 1 or 2n − 4. The parameters of the codes and their automorphism groups for any odd prime are obtained and PD-sets inside the symmetric group S_{n are found for full permutation decoding for all primes and all integers n ≥ 6.}