Binary Sequences of Arbitrary Length with Near-Ideal Correlation
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 p(p+2) 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 13, 1989
- Accession Number
- ADA209956
Entities
People
- Patrick R. Hirschler-marchand
Organizations
- Massachusetts Institute of Technology