Construction-D lattice from Garcia–Stichtenoth tower code

We show an explicit construction of an efficiently decodable family of n -dimensional lattices whose minimum distances achieve Ω ( n / ( log n ) ε + o ( 1 ) ) for ε > 0 . It improves upon the state-of-the-art construction due to Mook–Peikert (IEEE Trans Inf Theory 68(2):863–870, 2022) that provid...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2024-05, Vol.92 (5), p.1127-1142
Main Authors: Kirshanova, Elena, Malygina, Ekaterina
Format: Article
Language:English
Subjects:
BCH codes
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Lattices
Soft decision decoding
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Summary:We show an explicit construction of an efficiently decodable family of n -dimensional lattices whose minimum distances achieve Ω ( n / ( log n ) ε + o ( 1 ) ) for ε > 0 . It improves upon the state-of-the-art construction due to Mook–Peikert (IEEE Trans Inf Theory 68(2):863–870, 2022) that provides lattices with minimum distances Ω ( 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 49(11):2809–2825, 2003) to algebraic-geometric codes.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-023-01333-2