Multilevel and multidimensional Hadamard matrices

Multilevel Hadamard matrices (MHMs), whose entries are integers as opposed to the traditional restriction to {±1}, were introduced by Trinh, Fan, and Gabidulin in 2006 as a way to construct multilevel zero-correlation zone sequences, which have been studied for use in approximately synchronized code...

Full description

Saved in:
Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2009-06, Vol.51 (3), p.245-252
Main Authors: Adams, Sarah Spence, Crawford, Matthew, Greeley, Caitlin, Lee, Bryce, Murugan, Mathav Kishore
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Multilevel Hadamard matrices (MHMs), whose entries are integers as opposed to the traditional restriction to {±1}, were introduced by Trinh, Fan, and Gabidulin in 2006 as a way to construct multilevel zero-correlation zone sequences, which have been studied for use in approximately synchronized code division multiple access systems. We answer the open question concerning the maximum number of distinct elements permissible in an order n MHM by proving the existence of an order n MHM with n elements of distinct absolute value for all n . We also define multidimensional MHMs and prove an analogous existence result.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-008-9258-7