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 ...

We prove that for $n$ sufficiently large, all perfect 3-hash linear codes in notation="LaTeX">$\mathbb {F}_{3}^{n}$ must have dimension at most notation="LaTeX">$\left ({\frac {1}{4}-\epsilon }\right)n$ some absolute constant notation...