Cent. Eur. J. Math. • 9(6) • 2011 • 1411-1423 DOI: 10.2478/s11533-011-0072-5 Codes and designs from triangular graphs and their line graphs Washiela Fish 1∗ , Khumbo Kumwenda 1† , Eric Mwambene 1‡ 1 Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa For any prime p, we consider p-ary linear codes obtained from the span over F 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. 05-XX, 94B05, 94B35 Automorphism group • Incidence design • Incidence matrix • Line graph • Linear code • Permutation decoding • Triangular graph © Versita Sp. z o.o. 1. Introduction Linear codes from the row span of incidence and adjacency matrices of various regular graphs have received considerable attention recently (see [4, 9, 13–15] for examples). In particular, codes from incidence matrices of complete graphs K n have been examined in [14]. They are shown to have some properties similar to those of codes from adjacency matrices of their line graphs, the triangular graphs, considered by Haemers, Peeters and van Rijckevorsel in [9], Key, Moori and Rodrigues in [13, 19], and Tonchev in [20]. For instance, they inherit the automorphism group of the graph, their minimum words are scalar multiples of rows of their generator matrices and they permit permutation decoding. An obvious question is whether similar properties hold with codes generated by incidence matrices of triangular graphs and adjacency matrices of their line graphs. We show that this is the case to a large extent. ∗ E-mail: wfish@uwc.ac.za † E-mail: khumbo@aims.ac.za ‡ E-mail: emwambene@uwc.ac.za