More efficient bounded-distance decoding of the Golay code and the Leech lattice

Abstract

New multilevel constructions of the Leech lattice and the Golay code are presented. They are derived from Turyn's constructions and the 'holy construction' with the octacode as the glue code. Further, we show that the 'holy construction' of the Leech lattice with the octacode as the glue code is essentially different from the permuted Turyn construction, although both constructions rely on the octacode. Based on these structures, more efficient bounded-distance decoding algorithms of the Golay code and the Leech lattice are presented.<>