There are no good infinite families of toric codes
<|reference_start|>There are no good infinite families of toric codes: 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 Szemer\'edi-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.<|reference_end|>
@article{bell2024there,
    title={There are no good infinite families of toric codes},
    author={Jason P. Bell, Sean Monahan, Matthew Satriano, Karen Situ, Zheng Xie},
    journal={arXiv preprint arXiv:2406.00243},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.00243},
    primaryClass={math.CO cs.IT math.AG math.IT}
}