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11/02/2022
Exact Completeness of LP Hierarchies for Linear Codes
Determining the maximum size A_2(n,d) of a binary code of blocklength n ...
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09/15/2022
Almost Ramanujan Expanders from Arbitrary Expanders via Operator Amplification
We give an efficient algorithm that transforms any bounded degree expand...
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12/16/2021
A Complete Linear Programming Hierarchy for Linear Codes
A longstanding open problem in coding theory is to determine the best (a...
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12/02/2021
Explicit Abelian Lifts and Quantum LDPC Codes
For an abelian group H acting on the set [ℓ], an (H,ℓ)-lift of a graph G...
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11/11/2020
Unique Decoding of Explicit ε-balanced Codes Near the Gilbert-Varshamov Bound
The Gilbert-Varshamov bound (non-constructively) establishes the existen...
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11/11/2020
List Decoding of Direct Sum Codes
We consider families of codes obtained by "lifting" a base code 𝒞 throug...
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09/03/2020
Sum-of-Squares Lower Bounds for Sherrington-Kirkpatrick via Planted Affine Planes
The Sum-of-Squares (SoS) hierarchy is a semi-definite programming meta-a...
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07/11/2020
Tighter Bounds on the Independence Number of the Birkhoff Graph
The Birkhoff graph ℬ_n is the Cayley graph of the symmetric group S_n, w...
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07/18/2019