Bounds on Codes Based on Graph Theory
Information Theory
2008-07-01 v1 math.IT
Abstract
Let be the maximum order (maximum number of codewords) of a -ary code of length and Hamming distance at least . And let that of a binary code of constant weight . Building on results from algebraic graph theory and Erd\H{o}s-ko-Rado like theorems in extremal combinatorics, we show how several known bounds on and can be easily obtained in a single framework. For instance, both the Hamming and Singleton bounds can derived as an application of a property relating the clique number and the independence number of vertex transitive graphs. Using the same techniques, we also derive some new bounds and present some additional applications.
Cite
@article{arxiv.0806.4979,
title = {Bounds on Codes Based on Graph Theory},
author = {Salim Y. El Rouayheb and C. N. Georghiades and E. Soljanin and A. Sprintson},
journal= {arXiv preprint arXiv:0806.4979},
year = {2008}
}