Title: On some invariances of left and right autocorrelation functions of sequences over the quaternions
Authors: Oleg Kuznetsov
Addresses: School of Mathematical Sciences, Monash University, Clayton campus, Wellington Road, Clayton, Victoria 3800, Australia
Abstract: We study the relation between the left and the right autocorrelation functions of a sequence over the algebra of real quaternions ℍ. We have found that the real parts of the corresponding left and right autocorrelation values are equal for any sequence. Also, the sum of the norms of all left autocorrelation values is equal to the sum of the norms of all right autocorrelation values. Equivalence of left and right perfection and almost perfection over quaternions is a simple consequence of our results.
Keywords: quaternions; left autocorrelation; right autocorrelation; left perfect; right perfect; invariances; sequences.
International Journal of Information and Coding Theory, 2013 Vol.2 No.2/3, pp.105 - 114
Received: 23 Jul 2012
Accepted: 27 Mar 2013
Published online: 07 Mar 2014 *