Decompositions of Edge-Colored Digraphs: A New Technique in the Construction of Constant-Weight Codes and Related Families
Yeow Meng Chee, Fei Gao, Han Mao Kiah, Alan Chi Hung Ling, Hui Zhang,, Xiande Zhang
TL;DR
This paper introduces a novel technique using edge-colored digraph decompositions to achieve asymptotically exact Johnson-type bounds for various classes of constant-weight and related codes.
Contribution
It presents a new method leveraging digraph decompositions to improve bounds in coding theory, specifically for constant-weight and related codes.
Findings
Johnson-type bounds are asymptotically exact for several code classes
Edge-colored digraph decomposition is an effective tool in coding theory
The technique applies to constant-composition, nonbinary, and multiply constant-weight codes
Abstract
We demonstrate that certain Johnson-type bounds are asymptotically exact for a variety of classes of codes, namely, constant-composition codes, nonbinary constant-weight codes and multiply constant-weight codes. This was achieved via an interesting application of the theory of decomposition of edge-colored digraphs.
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Taxonomy
TopicsCoding theory and cryptography · Error Correcting Code Techniques · Cooperative Communication and Network Coding