Codes associated with triangular graphs and permutation decoding

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.