Discrete Mathematics for Communications Systems.
Abstract
A Costas array is an nxn array of dots and blanks with exactly one dot in each row and column, and with distinct vector differences between all pairs of dots. As a frequency-hop pattern for radar or sonar, a Costas array has an optimum ambiguity function, since any translation of the array parallel to the coordinate axes produces at most one out-of-phase coincidence. We conjecture that nxn Costas array exist for every positive integer n. Using various constructions due to L. Welch, A. Lempel, and the authors, Costas arrays are shown to exist when n = p - 1, n = q - 2, n = q - 3, and sometimes when n = q - 4 and n = q - 5, where p is a prime number, and q is any power of a prime number.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 31, 1985
- Accession Number
- ADA152814
Entities
People
- S. W. Golomb
Organizations
- University of Southern California