On optimal codes for binary asymmetric channels (Corresp.)

Let{ v_{1}, cdots , v_{N} }be a code ofNvectors whose components consist ofmones and(n - m)zeros. The vectors are transmitted with equal probability over the asymmetric channel whose error probabilities for transmitted zeros and ones equal respectively0andp, 0 < p < 1(such channels arise in optical communication). The problem of determining for fixed values of the parametersN, n, m, pthose codes which achieve minimum error probability is studied. The problem is solved forN leq 3. Partial results are obtained for allN.