Accession Number:

ADA209956

Title:

Binary Sequences of Arbitrary Length with Near-Ideal Correlation

Descriptive Note:

Technical rept.

Corporate Author:

MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

Personal Author(s):

Report Date:

1989-06-13

Pagination or Media Count:

31.0

Abstract:

Binary sequences having two-valued correlation are very much sought after. Their applications are found in many areas such as error-correcting codes, synchronization, spread-spectrum communication, time resolution measurements, ranging, picture transmission, acoustics, radar, and antenna design. Many sequences are known to have two-valued periodic correlation. Perhaps, the most famous of these are maximum-length sequences. Maximum-length sequences have two-valued periodic correlations and power spectra. They satisfy linear recursions which are a consequence of Galois field theory and are very easily implemented with linear shift registers. Barker sequences have correlations less than or equal to 1, except at the origin. Twin-prime p,p 2 sequences have correlation of pp2 at the origin and -1 elsewhere. Hall sequences and quadratic-residue or Legendre sequences also have the same two- valued periodic correlations and power spectra. The above sequences have remarkable correlation properties but only come in certain lengths. Specifically, this report develops 1 A dense class of binary sequences, called Mac sequences having arbitrary length and ideal correlation properties over a limited range around the peak and 2 A general algorithm to construct Mac sequences of any length.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE