A new formula for the minimum distance of an expander code

Year 2022, Volume: 9 Issue: 2, 9 - 14, 13.05.2022

Sudipta Mallik

https://doi.org/10.13069/jacodesmath.1111379

Abstract

An expander code is a binary linear code whose parity-check matrix is the bi-adjacency matrix of a bipartite expander graph. We provide a new formula for the minimum distance of such codes. We also provide a new proof of the result that $2(1-\varepsilon) \gamma n$ is a lower bound of the minimum distance of the expander code given by an $(m,n,d,\gamma,1-\varepsilon)$ expander bipartite graph.

Keywords

Linear code, Minimum distance, Expander graph, Adjacency matrix

References

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