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We construct quantum locally testable codes (LTCs) with constant rate, distance, soundness and locality under a variant of a product expansion conjecture of Bafna and Vyas (2026) about Reed-Solomon codes. In particular, we use the high-dimensional expansion framework of Dinur, Lin and Vidick (2024) for constructing quantum LTCs, instantiated with ... more >>>
The Remote Point Problem (RPP) is an algorithmic problem that asks, given a linear subspace $L \subseteq \mathbb{F}^n$ of dimension $k$, to deterministically find a vector $v \in \mathbb{F}^n$ far in Hamming distance from $L$. This problem was introduced by Alon, Panigrahy and Yekhanin [APY09], motivated in part by the ... more >>>
Sipser and Spielman constructed LDPC codes from either bipartite \emph{spectral} expanders or one-sided \emph{lossless} expanders.
In higher dimensions, \emph{spectral} expansion similarly played a central role in the constructions of asymptotically good classical LTCs and qLDPC codes by Dinur, Evra, Livne, Lubotzky, and Mozes and by Panteleev and Kalachev.
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