[Resource Topic] 2023/1730: Construction-D lattice from Garcia-Stichtenoth tower code

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Construction-D lattice from Garcia-Stichtenoth tower code

Authors: Elena Kirshanova, Ekaterina Malygina


We show an explicit construction of an efficiently decodable family of n-dimensional lattices whose minimum distances achieve \Omega(\sqrt{n} / (\log n)^{\varepsilon+o(1)}) for \varepsilon>0. It improves upon the state-of-the-art construction due to Mook-Peikert (IEEE Trans.\ Inf.\ Theory, no. 68(2), 2022) that provides lattices with minimum distances \Omega(\sqrt{n/ \log n}). These lattices are construction-D lattices built from a sequence of BCH codes. We show that replacing BCH codes with subfield subcodes of Garcia-Stichtenoth tower codes leads to a better minimum distance. To argue on decodability of the construction, we adapt soft-decision decoding techniques of Koetter-Vardy (IEEE Trans.\ Inf.\ Theory, no.\ 49(11), 2003) to algebraic-geometric codes.

ePrint: https://eprint.iacr.org/2023/1730

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