Optimal Small Set Expanders and Their Codes
Resumen:
A left-regular bipartite graph G of degree d is called a (t,alpha)-small-set-expander if every subset X of left vertices of size at most t has at least alpha*|X| neighbors. Such a graph is an optimal small-set expander if small subsets have as many neighbors as possible. We characterize optimal expanders combinatorially via girth and prove the existence of s-optimal expanders for every s. We also prove that s-optimality yields new "transfer" lower bounds on the number of neighbors of sets of size h greater than or equal to s. Finally, as an application, we discuss the use of optimal small-set expanders in building good codes for key exchange protocols in post-quantum cryptography.
| 2026 | |
| Agencia Nacional de Investigación e Innovación | |
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Expander graphs Post-quantum cryptography Expander codes Small set expansion LDPC codes Post-quantum cryptograph Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
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| Inglés | |
| Agencia Nacional de Investigación e Innovación | |
| REDI | |
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https://hdl.handle.net/20.500.12381/5721
https://arxiv.org/pdf/2606.23579 |
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| Acceso abierto | |
| Reconocimiento-NoComercial 4.0 Internacional. (CC BY-NC) |
