On nested completely regular codes and distance regular graphs

Abstract

Publicació amb motiu de la 14th International Workshop on Algebraic and Combinatorial Coding Theory (September 7-13, 2014, Svetlogorsk, Russia)

Infinite families of linear binary nested completely regular codes with covering radius ρ equal to 3 and 4 are constructed. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter D = 3 or 4 are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive.