Title: A method of constructing a quaternion perfect sequence using composition of sequences of even lengths
Authors: Oleg Kuznetsov; Thomas Eric Hall
Addresses: School of Mathematical Sciences, Monash University, Clayton Campus, Wellington Road, Clayton, Victoria 3800, Australia ' School of Mathematical Sciences, Monash University, Clayton Campus, Wellington Road, Clayton, Victoria 3800, Australia
Abstract: We introduce a new method of composition of two sequences of even lengths which results in obtaining a perfect sequence of longer length. Based on our result, we have developed an algorithm of constructing perfect sequences by combination of three perfect sequences of shorter length, which can be used for significant reduction in the computer time required for finding new perfect sequences of even lengths, in comparison with performing an exhaustive computer search over sequences of the same length. The new method has been applied to sequences over quaternion roots of unity, and new perfect sequences over 12-quaternion roots of unity have been obtained. Some examples, demonstrating the use of the method, are provided.
Keywords: quaternions; quaternion roots of unity; perfect sequences; right perfect; composition of sequences; even lengths.
International Journal of Information and Coding Theory, 2013 Vol.2 No.2/3, pp.67 - 83
Received: 14 Oct 2011
Accepted: 08 Jun 2012
Published online: 07 Mar 2014 *