Properties of codes with two homogeneous weights

Abstract

Delsarte showed that for any projective linear code over a finite field GF(pr) with two nonzero Hamming weights w1<w2 there exist positive integers u and s such that w1=psu and w2=ps(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 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). This gives a new proof of the known result that any such code yields a strongly regular graph. We apply these results to existence questions on two-weight codes.