论文信息 - Double circulant constructions of the Leech lattice

Double circulant constructions of the Leech lattice

Abstract 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.

Robin Chapman | R. Chapman

[1] Wolfgang Ebeling,et al. Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch , 1994 .

[2] John H. Conway,et al. A characterisation of Leech's lattice , 1969 .

[3] N. Sloane,et al. Double Circulant Codes over $$\mathbb{Z}_4 $$ and Even Unimodular Lattices , 1997 .

[4] Masaaki Harada,et al. Self-Dual Codes over Z 4 and Unimodular Lattices : A Survey , 2002 .

[5] N. Sloane,et al. Double Circulant Codes over Z 4 and Even Unimodular Lattices , 1997 .

[6] A. Robert Calderbank,et al. Quaternary quadratic residue codes and unimodular lattices , 1995, IEEE Trans. Inf. Theory.

[7] J. Leech. Notes on Sphere Packings , 1967, Canadian Journal of Mathematics.

[8] John McKay. A Setting for the Leech Lattice , 1973 .

[9] Bruno Schoeneberg,et al. Elliptic Modular Functions , 1974 .