Bounds on Codes Based on Graph Theory

"THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD" Let Aq(n, d) be the maximum order (maximum number of codewords) of a q-ary code of length n and Hamming distance at least d; A(n, d, w) that of a binary code of constant weight w. Building on results from algebraic graph theory and Erdos-ko-Rado like theorems in extremal combinatorics, we show how several known bounds on Aq(n, d) and A(n, d, w) 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.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Salim Y. El Rouayheb, Costas N. Georghiades, Emina Soljanin, Alexander Sprintson
• Keywords: Algebraic Graph Theory, CORR 2008, Education, Maximum Number, STUDENT PAPER AWARD