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Parameterization of Perfect Sequences over a Composition Algebra
Takao MAEDA Takafumi HAYASHI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E95A
No.12
pp.21392147 Publication Date: 2012/12/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E95.A.2139
Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Sequence Keyword: parameterization, perfect sequence, autocorrelation, composition algebra, quaternion, octonion,
Full Text: PDF>>
Summary:
A parameterization of perfect sequences over composition algebras over the real number field is presented. According to the proposed parameterization theorem, a perfect sequence can be represented as a sum of trigonometric functions and points on a unit sphere of the algebra. Because of the noncommutativity of the multiplication, there are two definitions of perfect sequences, but the equivalence of the definitions is easily shown using the theorem. A composition sequence of sequences is introduced. Despite the nonassociativity, the proposed theorem reveals that the composition sequence from perfect sequences is perfect.

