Completely Regular Codes in Distance Regular Graphs
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics;
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Product details:
- Edition number 1
- Publisher Chapman and Hall
- Date of Publication 13 March 2025
- ISBN 9781032494449
- Binding Hardback
- No. of pages520 pages
- Size 254x178 mm
- Weight 1120 g
- Language English
- Illustrations 11 Illustrations, black & white; 11 Line drawings, black & white 587
Categories
Short description:
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.
MoreLong description:
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
Table of Contents:
1. Completely regular codes and equitable partitions. 2. Completely regular codes over finite fields. 3. Completely regular codes in the Johnson graph. 4. Codes over rings and modules. 5. Group actions on codes in graphs. 6. Some completely regular codes in Doob graphs. 7. Completely regular codes: tables of small parameters for binary and ternary Hamming graphs.
