Some new results on binary asymmetric error-correcting codes

Let C(n,δAs) denote a binary, asymmetric error-correcting code of length n and asymmetric minimum distance dAs. Such a code is called optimal, if it has maximum size. This maximum size is denoted by AAs(n,dAs,) It is shown that there exist exactly four non-isomorphic optimal C(3,2) codes, four non-isomorphic optimal C(5,2) codes and twelve non-isomorphic optimal C(7,2) codes. Further it is proved that optimal C(n, 2) codes of length n=2,4,6 and 8 must be unique. The sizes of all theses codes are given in the following table