On the Parameters of Codes with Two Homogeneous Weights

Delsarte showed that for any projective linear code over a finite field GF (p) with two nonzero Hamming weights w1 < w2 there exist positive integers u and s such that w1 = p u and w2 = p (u + 1). Moreover, he showed that the additive group of such a code has a strongly regular Cayley graph. Here we show that for any proper, regular, projective linear code C over a finite Frobenius ring with two integral nonzero homogeneous weights w1 < w2 there is a positive integer d, a divisor of |C|, and positive integer u such that w1 = du and w2 = d(u+1). In doing so, we present a new proof that any such code yields a strongly regular graph.