New explicit binary constant weight codes from Reed-Solomon codes

Binary constant weight codes have important applications 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 a new construction of explicit binary constant weight codes from q-ary ReedSolomon codes. Some of our binary constant weight codes are optimal or new. In particular new binary constant weight codes A(64, 10, 8) ≥ 4108 and A(64, 12, 8) ≥ 522 are constructed. We also give explicitly constructed binary constant weight codes which improve Gilbert and Graham-Sloane lower bounds in some range of parameters. An extension to algebraic geometric codes is also presented.