New families of completely regular codes and their corresponding distance regular coset graphs

Abstract

In this paper three new infinite families of linear binary completely regular codes are constructed. They have covering radius ? = 3 and 4, and are halves of binary Hamming and binary extended Hamming codes of length n = 2 m ?1 and 2 m , where m is even. There are also shown some combinatorial (binomial) identities which are new, to our knowledge.These completely regular codes induce, in the usual way, i.e., as coset graphs, three infinite families of distance-regular graphs of diameter three and four. This description of such graphs is new.