BCH codes are good for distance multicolorings with radio frequencies in hypercubes asymptotically

It is announced that binary primitive narrow-sense BCH codes or their shortenings have size asymptotically within a constant factor below the largest possible size among binary codes of the same length, n, and the same minimum distance, d, as n → ∞ while d is constant. Consequently the asymptotic growth of distance multicoloring parameters in hypercubes is determined. Connections with radio frequencies allocation problem are discussed