On the number of q-ary quasi-perfect codes with covering radius 2

Abstract

In this paper we present a family of q-ary nonlinear quasi-perfect codes with covering radius 2. The codes have length $$n = q^m$$ and size $$ M = q^{n - m - 1}$$ where q is a prime power, $$q \ge 3$$ , m is an integer, $$m \ge 2$$ . We prove that there are more than $$q^{q^{cn}}$$ nonequivalent such codes of length n, for all sufficiently large n and a constant $$c = \frac{1}{q} - \varepsilon $$ .