Title :
Multilevel perfect sequences over integers
Author :
Li, Xiao Dong ; Fan, P.Z. ; Mow, Wai Ho ; Darnell, M.
Author_Institution :
Sch. of Math. & Comput. Eng., Xihua Univ., Chengdu, China
Abstract :
Multilevel perfect sequences over integers are introduced which include the conventional binary perfect sequences as special cases. Such sequences can be derived from multilevel cyclic Hadamard matrices over integers. It is proved that integer-valued perfect sequences of odd lengths with the energy being non-square integers do not exist, and the existence of four-level perfect sequences of lengths up to 11 over the alphabet sets {±1, ±2} and {±1, ±3} is completely determined.
Keywords :
Hadamard matrices; binary sequences; alphabet set; binary perfect sequence; four-level perfect sequence; integer-valued perfect sequence; multilevel cyclic Hadamard matrices; multilevel perfect sequence; nonsquare integer;
Journal_Title :
Electronics Letters
DOI :
10.1049/el.2010.3634
