A catalog of minimally nonideal matrices

This paper describes a backtracking algorithm for the enumeration of nonisomorphic minimally nonideal (n × n) matrices that are not degenerate projective planes. The application of this algorithm for n ⩽ 12 yielded 20 such matrices, adding 5 matrices to the 15 previously known. For greater dimensions, n = 14 and n = 17, 13 new matrices are given. For nonsquare matrices, 38 new minimally nonideal matrices are desribed.