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Double circulant constructions of the Leech lattice

Part of: Geometry of numbers Theory of error-correcting codes and error-detecting codes

Published online by Cambridge University Press:  09 April 2009

Robin Chapman
Robin Chapman
Affiliation:
School of Mathematical Sciences University of ExeterExeter EX4 4QEUK e-mail: rjc@maths.ex.ac.uk
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Abstract

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We consider the problem of finding, for each even number m, a basis of orthogonal vectors of length in the Leech lattice. We give such a construction by means of double circulant codes whenever m = 2p and p is a prime not equal to 11. From this one can derive a construction for all even m not of the form 2· 11r.

MSC classification

Secondary: 11H06: Lattices and convex bodies 11H71: Relations with coding theory 94B05: Linear codes, general
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 3 , December 2000 , pp. 287 - 297
Copyright
Copyright © Australian Mathematical Society 2000

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