Codes and designs from triangular graphs and their line graphs

Abstract

Abstract For any prime p, we consider p-ary linear codes obtained from the span over $\mathbb{F}_p $ p of rows of incidence matrices of triangular graphs, differences of the rows and adjacency matrices of line graphs of triangular graphs. We determine parameters of the codes, minimum words and automorphism groups. We also show that the codes can be used for full permutation decoding.