Remark on balanced incomplete block designs, near-resolvable block designs, and q-ary constant-weight codes

Abstract

We prove that any balanced incomplete block design B(v, k, 1) generates a nearresolvable balanced incomplete block design NRB(v, k − 1, k − 2). We establish a one-to-one correspondence between near-resolvable block designs NRB(v, k −1, k −2) and the subclass of nonbinary (optimal, equidistant) constant-weight codes meeting the generalized Johnson bound.