Asymptotic bound on binary self-orthogonal codes

We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the information rate R = 1/2, by our constructive lower bound, the relative minimum distance δ ≈ 0.0595 (for GV bound, δ ≈ 0.110). Moreover, we have proved that the binary self-orthogonal codes asymptotically achieve the Gilbert-Varshamov bound.