A Turyn-based neural Leech decoder

A new decoder for the Leech lattice is presented. This quasioptimal decoder utilizes a re-encoding paradigm, where candidates are obtained via a shallow neural network. This implies easy parallelization and low latency. The decoder exploits the fact that the Leech lattice is obtained from the direct sum of three polarized Gosset 8-dimensional lattices. This Turyn’s construction was used in 2010 by G. Nebe to build the extremal even unimodular lattice in dimension 72 from three copies of the Leech lattice. Thus, we view this work as a first step towards the implementation of an efficient decoder for the Nebe 72-dimensional lattice.

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