On a family of binary completely transitive codes with growing covering radius

A new family of binary linear completely transitive (and, therefore, completely regular) codes is constructed. The covering radius of these codes is growing with the length of the code. In particular, for any integer r > 1, there exist two codes with d=3, covering radius r and length 2r(4r-1) and (2r+1)(4r+1), respectively. These new completely transitive codes induce, as coset graphs, a family of distance-transitive graphs of growing diameter.Comment: Submitted to Discrete mathematics. March 10, 201

On Completely Regular Codes

This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are established. In particular, we present a few new results on completely regular codes with covering radius 2 and on extended completely regular codes