A method of constructing a quaternion perfect sequence using composition of sequences of even lengths. (1st January 2013)

• Record Type: Journal Article
• Authors: Kuznetsov, Oleg; Hall, Thomas Eric
• Is Part Of: International journal of information and coding theory. Volume 2:Number 2/3(2013)
• Page Start: 67
• Page End: 83
• Publication Date: 2013-01-01
• Subjects: quaternion -- perfect sequence -- right perfect -- composition of sequences; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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.