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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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.
📌 3 Key Takeaways
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Objective & Hypothesis:An expander code is a binary linear code whose parity-check matrix is the bi-adjacency matrix of a bipartite expander graph.
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Key Findings & Data:We provide a new formula for the minimum distance of such codes.
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Conclusion & Impact: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.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Linear code · Minimum distance · Expander graph
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.
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Cite This Article
Mallik, S. (2022). A new formula for the minimum distance of an expander code. Journal of Algebra Combinatorics Discrete Structures and Applications, Cilt: 9 Sayı: 2, 9–14. https://doi.org/10.13069/jacodesmath.1111379