A lower bound for ternary constant weight codes

摘要

We derive a lower bound for ternary constant-weight codes with minimum Hamming distance three. The bound is similar to a bound for binary constant-weight codes with minimum distance four described by Graham and Sloane (1980). It improves upon the Gilbert (1952) bound and coincides asymptotically with the Johnson (1962) bound for fixed weight as the codeword length tends to infinity.