Codes from lattice and related graphs, and permutation decoding

Codes of length n2n2 and dimension 2n−12n−1 or 2n−22n−2 over the field FpFp, for any prime pp, that can be obtained from designs associated with the complete bipartite graph Kn,nKn,n and its line graph, the lattice graph, are examined. The parameters of the codes for all primes are obtained and PD-sets are found for full permutation decoding for all integers n≥3n≥3.