EISENSTEIN LATTICES, GALOIS RINGS AND QUATERNARY CODES-Reference-Cited by-同舟云学术

EISENSTEIN LATTICES, GALOIS RINGS AND QUATERNARY CODES

Published:2006-06 Issue:02 Volume:02 Page:289-303
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

GABORIT PHILIPPE¹,NATIVIDAD ANN MARIE²,SOLÉ PATRICK³

Affiliation:

1. LACO, Université de Limoges, 123 rue Albert Thomas, 87 Limoges, France

2. Department of Mathematics, University of the Philippines, Diliman, 1101 Quezon City, Philippines

3. CNRS, I3S ESSI, BP 145 Route des Colles, 06 903 Sophia Antipolis, France

Abstract

Self-dual codes over the Galois ring GR(4,2) are investigated. Of special interest are quadratic double circulant codes. Euclidean self-dual (Type II) codes yield self-dual (Type II) ℤ4-codes by projection on a trace orthogonal basis. Hermitian self-dual codes also give self-dual ℤ4-codes by the cubic construction, as well as Eisenstein lattices by Construction A. Applying a suitable Gray map to self-dual codes over the ring gives formally self-dual 𝔽4-codes, most notably in length 12 and 24. Extremal unimodular lattices in dimension 38, 42 and the first extremal 3-modular lattice in dimension 44 are constructed.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042106000577

Reference14 articles.

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2. Jacobi forms over totally real fields and type II codes over Galois rings GR(2m,f)

3. Quaternary quadratic residue codes and unimodular lattices

4. Eisenstein lattices, Galois rings, and theta series

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