Certain self-dual codes over ℤ4 and the odd leech lattice

T. Aaron Gulliver; Masaaki Harada

doi:10.1007/3-540-63163-1_10

Certain self-dual codes over ℤ₄ and the odd leech lattice

T. Aaron Gulliver, Masaaki Harada

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Citations (Scopus)

Abstract

Recently, alternative constructions of the Leech lattice and the shorter Leech lattice have been discovered using self-dual codes over ℤ₄. In this paper, we provide a classification of length 24 double circulant Type I codes over ℤ₄ with minimum Euclidean weight 12. These codes determine (via Construction A₄) the odd Leech lattice, which is a unique 24-dimensional odd unimodular lattice with minimum norm 3.

Original language	English
Title of host publication	Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 12th International Symposium, AAECC- 12, Proceedings
Editors	Teo Mora, Harold Mattson
Publisher	Springer-Verlag
Pages	130-137
Number of pages	8
ISBN (Print)	3540631631, 9783540631637
DOIs	https://doi.org/10.1007/3-540-63163-1_10
Publication status	Published - 1997 Jan 1
Externally published	Yes
Event	12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1997 - Toulouse, France Duration: 1997 Jun 23 → 1997 Jun 27

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1255
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1997
Country/Territory	France
City	Toulouse
Period	97/6/23 → 97/6/27

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-63163-1_10

Cite this

Gulliver, T. A., & Harada, M. (1997). Certain self-dual codes over ℤ₄ and the odd leech lattice. In T. Mora, & H. Mattson (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 12th International Symposium, AAECC- 12, Proceedings (pp. 130-137). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1255). Springer-Verlag. https://doi.org/10.1007/3-540-63163-1_10

Certain self-dual codes over ℤ₄ and the odd leech lattice. / Gulliver, T. Aaron; Harada, Masaaki.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 12th International Symposium, AAECC- 12, Proceedings. ed. / Teo Mora; Harold Mattson. Springer-Verlag, 1997. p. 130-137 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1255).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Gulliver, TA & Harada, M 1997, Certain self-dual codes over ℤ₄ and the odd leech lattice. in T Mora & H Mattson (eds), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 12th International Symposium, AAECC- 12, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1255, Springer-Verlag, pp. 130-137, 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1997, Toulouse, France, 97/6/23. https://doi.org/10.1007/3-540-63163-1_10

Gulliver TA, Harada M. Certain self-dual codes over ℤ₄ and the odd leech lattice. In Mora T, Mattson H, editors, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 12th International Symposium, AAECC- 12, Proceedings. Springer-Verlag. 1997. p. 130-137. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-63163-1_10

Gulliver, T. Aaron ; Harada, Masaaki. / Certain self-dual codes over ℤ₄ and the odd leech lattice. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 12th International Symposium, AAECC- 12, Proceedings. editor / Teo Mora ; Harold Mattson. Springer-Verlag, 1997. pp. 130-137 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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