A class of perfect ternary constant-weight codes (Q1591634)

A class of perfect ternary constant-weight codes of length \(2^r\), weight \(2^r-1\) and minimum distance 3 is presented. The construction is based on binary Hamming codes. The number of codewords is \(2^{2^r}-1\). For \(r=2\), the construction results in the subcode of the \([4,2,3]\) tetracode consisting of its nonzero codewords. These are the only perfect \(q\)-ary constant-weight codes known to date. These codes can be shortened twice to give two more classes of optimal codes.