On systematic single asymmetric error correcting codes

Summary form only given. In the asymmetric channel it is assumed that the transmitted binary sequence may suffer errors of one type only, say 1→0; the 0→1 errors are rare. Since errors are of one type they are called asymmetric errors as opposed to symmetric errors in which both 1→0 and 0→1 are expectable. Obviously, any symmetric error correcting code is also an asymmetric error correcting code. One would expect to obtain systematic asymmetric error correcting codes that have higher information rate than the symmetric ones; however, this is mostly not the case. We show in this paper that for any code dimension n (except for n=2^r and n=2^r1 where r is a positive integer) the systematic asymmetric error correcting codes are not better than the symmetric codes