International Journal of Combinatorics
Volume 2011 (2011), Article ID 937941, 15 pages
doi:10.1155/2011/937941
Research Article

Classification of Normal Sequences

Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

Received 4 August 2010; Accepted 13 January 2011

Academic Editor: Gerard Jennhwa Chang

Copyright © 2011 Dragomir Ž. Ðoković. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Base sequences B S ( 𝑚 , 𝑛 ) are quadruples ( 𝐴 ; 𝐵 ; 𝐶 ; 𝐷 ) of { ± 1 } -sequences, with 𝐴 and 𝐵 of length 𝑚 and 𝐶 and 𝐷 of length 𝑛 , such that the sum of their nonperiodic autocorrelation functions is a 𝛿 -function. Normal sequences N S ( 𝑛 ) are base sequences ( 𝐴 ; 𝐵 ; 𝐶 ; 𝐷 ) B S ( 𝑛 , 𝑛 ) such that 𝐴 = 𝐵 . We introduce a definition of equivalence for normal sequences N S ( 𝑛 ) and construct a canonical form. By using this canonical form, we have enumerated the equivalence classes of N S ( 𝑛 ) for 𝑛 4 0 .