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arXiv · 2406.00243

There are no good infinite families of toric codes

Jason P. Bell·Sean Monahan·Matthew Satriano·Karen Situ·Zheng Xie
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Abstract

Soprunov and Soprunova introduced the notion of a good infinite family of toric codes. We prove that such good families do not exist by proving a more general Szemerédi-type result: for all $c\in(0,1]$ and all positive integers $N$, subsets of density at least $c$ in $\{0,1,\dots,N-1\}^n$ contain hypercubes of arbitrarily large dimension as $n$ grows.

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Jason P. Bell, Sean Monahan, Matthew Satriano, Karen Situ, Zheng Xie. 2025-01-17. There are no good infinite families of toric codes. https://arxiv.org/abs/2406.00243

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