Perfect Codes for Metrics Generated by Primitive 2-Error-Correcting Binary BCH Codes

For any positive integer m, a metric on $\mathbb F_2^{2m}$ is considered which is induced by the quasi-perfect $[2^m-1, 2^m-2m-1,5]$ binary BCH code. The isometry group is determined. Constructions of codes are given which are perfect with respect to this metric. In addition, easy decoding methods for these codes are proposed.