On a class of binary linear completely transitive codes with arbitrary covering radius

An infinite class of new binary linear completely transitive (and so, completely regular) codes is given. The covering radius of these codes is growing with the length of the code. In particular, for any integer ρ≥2ρ≥2, there exist two codes in the constructed class with d=3d=3, covering radius ρρ and lengths (2ρ2) and (2ρ+12), respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described.