Chapman & Hall/CRC Monographs and Research Notes in Mathematics Completely Regular Codes Distance Graphs

This book provides, for the first time, a definitive source for the main theoretical notions underpinning this fascinating area of study. It also supplies several useful surveys of constructions using Coding Theory, Design Theory and Finite Geometry in the various families of distance regular graphs of large diameters. The concept of completely regular codes was introduced by Delsarte in his celebrated 1973 thesis, which created the field of Algebraic Combinatorics. This notion was extended by several authors from classical codes over finite fields to codes in distance-regular graphs. Half a century later, there was no book dedicated uniquely to this notion. Most of Delsarte examples were in the Hamming and Johnson graphs. In recent years, many examples were constructed in other distance regular graphs including q-analogues of the previous, and the Doob graph. Completely Regular Codes in Distance Regular Graphs provides, for the first time, a definitive source for the main theoretical notions underpinning this fascinating area of study. It also supplies several useful surveys of constructions using coding theory, design theory and finite geometry in the various families of distance regular graphs of large diameters. Features Written by pioneering experts in the domain Suitable as a research reference at the master’s level Includes extensive tables of completely regular codes in the Hamming graph Features a collection of up-to-date surveys