Title: Codes associated with triangular graphs and permutation decoding

Authors: J.D. Key, J. Moori, B.G. Rodrigues

Addresses: 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

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 Sn are found for full permutation decoding for all primes and all integers n ≥ 6.

Keywords: linear codes; triangular graphs; permutation decoding; automorphism groups; automorphisms.

DOI: 10.1504/IJICOT.2010.032547

International Journal of Information and Coding Theory, 2010 Vol.1 No.3, pp.334 - 349

Published online: 06 Apr 2010 *

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