In this paper, we propose a novel construction for secure distributed matrix multiplication (SDMM) based on algebraic geometry (AG) codes, which we call the PoleGap SDMM scheme. The proposed construction is inspired by the GASP code, where so-called gaps in a certain polynomial are utilized to achieve higher communication rates. Our construction considers the gaps in a Weierstrass semigroup of a rational place in an algebraic function field to achieve a similar increase in the rate. This construction shows that there is potential in utilizing AG codes and their subcodes in SDMM since we demonstrate a better performance compared to state-of-the-art schemes in some parameter regimes.

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