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Paper:

TR25-066 | 21st May 2025 15:36

An Optimal Error-Correcting Reduction for Matrix Multiplication

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TR25-066
Authors: Shuichi Hirahara, Nobutaka Shimizu
Publication: 22nd May 2025 14:23
Downloads: 149
Keywords: 


Abstract:

We present an optimal ``worst-case exact to average-case approximate'' reduction for matrix multiplication over a finite field of prime order $p$. Any efficient algorithm that correctly computes, in expectation, at least $(\frac{1}{p} + \varepsilon)$-fraction of entries of the multiplication $A \cdot B$ of a pair $(A, B)$ of uniformly random matrices over the finite field of order $p$ for a positive constant $\varepsilon$ can be transformed into an efficient randomized algorithm that computes $A \cdot B$ for all the pairs $(A, B)$ of matrices with high probability. Previously, such reductions were known only in a low-error regime (Gola, Shinkar and Singh; RANDOM 2024) or under non-uniform reductions (Hirahara and Shimizu; STOC 2025).



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