Equidistant codes with distance 12

Abstract Let C be an equidistant binary code with m words, pairwise at distance 2 k , It is known that if C is not trivial then m ⩽ k 2 + k + 2. Furthermore equality is possible if and only if a projective plane of order k exists. This settles the problem of determining the maximal m for k ⩽10 with the exception of k = 6. In this paper we show that if k = 6 then m ⩽ 32, and we give an example of a code with m = 32. To settle the next unknown case, i.e. k = 10, one would first have to know whether a projective plane of order 10 exist.