# 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.

# Descriptors:

- *SEQUENCES(MATHEMATICS)
- *LENGTH
- *BINARY ARITHMETIC
- *APPLIED MATHEMATICS
- POWER SPECTRA
- RADAR
- TIME
- TRANSMITTANCE
- CORRELATION
- HIGH DENSITY
- ANTENNAS
- COMMUNICATION AND RADIO SYSTEMS
- ACOUSTICS
- PICTURES
- ERROR CORRECTION CODES
- SPREAD SPECTRUM
- FIELD THEORY
- RESOLUTION
- HALL EFFECT
- SHIFT REGISTERS
- ALGORITHMS
- MEASUREMENT

# Subject Categories:

- Numerical Mathematics