On optimal codes for binary asymmetric channels.

Let {nu(1),...,nu(n)} be a code of N vectors whose components consist of m ones and (n-m) zeros. The vectors are transmitted with equal probability over the asymmetric channel whose transmission probabilities for 0 ->1, 1->0 equal respectively 0 and p, 0 p 1 (such channels arise in optical communication). We study the problem of determining for fixed values of the parameters N, n, m, p those codes which achieve minimum error probability. The problem is solved for N =3. Partial results are obtained for all N.