Orthogonal Frames in the Leech Lattice and a Type II Code over Z22

T. Aaron Gulliver; Masaaki Harada

doi:10.1006/jcta.2000.3159

Orthogonal Frames in the Leech Lattice and a Type II Code over Z₂₂

T. Aaron Gulliver, Masaaki Harada

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper, we consider the problem of the existence of a basis of orthogonal vectors of norm 2k in the Leech lattice. Recently it has been shown that there is such a basis for every k (≥2) which is not of the form 11^r. In this paper, this problem is completely settled by finding such a basis for k=11. This is established by constructing an extremal Type II Z₂₂-code of length 24.

Original language	English
Pages (from-to)	185-188
Number of pages	4
Journal	Journal of Combinatorial Theory. Series A
Volume	95
Issue number	1
DOIs	https://doi.org/10.1006/jcta.2000.3159
Publication status	Published - 2001 Jul
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1006/jcta.2000.3159

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abstract = "In this paper, we consider the problem of the existence of a basis of orthogonal vectors of norm 2k in the Leech lattice. Recently it has been shown that there is such a basis for every k (≥2) which is not of the form 11r. In this paper, this problem is completely settled by finding such a basis for k=11. This is established by constructing an extremal Type II Z22-code of length 24.",

author = "Gulliver, {T. Aaron} and Masaaki Harada",

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N2 - In this paper, we consider the problem of the existence of a basis of orthogonal vectors of norm 2k in the Leech lattice. Recently it has been shown that there is such a basis for every k (≥2) which is not of the form 11r. In this paper, this problem is completely settled by finding such a basis for k=11. This is established by constructing an extremal Type II Z22-code of length 24.

AB - In this paper, we consider the problem of the existence of a basis of orthogonal vectors of norm 2k in the Leech lattice. Recently it has been shown that there is such a basis for every k (≥2) which is not of the form 11r. In this paper, this problem is completely settled by finding such a basis for k=11. This is established by constructing an extremal Type II Z22-code of length 24.

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Orthogonal Frames in the Leech Lattice and a Type II Code over Z₂₂

Abstract

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