New explicit binary constant weight codes from Reed-Solomon codes

Binary constant weight codes have important applications in various topics and have been studied for many years. Optimal or near-optimal binary constant weight codes of small lengths have been determined. In this paper we propose an improvement of the Ericson-Zinoviev construction of binary constant weight codes from q-ary codes. By applying this improvement to Reed-Solomon codes, some new or optimal binary constant weight codes are presented. In particular new binary constant weight codes A(64,10,8)≥4112 and A(64,12,8)≥522 are constructed. We also give explicitly constructed binary constant weight codes which improve the Gilbert and the Graham-Sloane lower bounds asymptotically in a small range of parameters. Some new binary constant weight codes constructed from algebraic-geometric codes by applying our this improvement are also presented.