This project will use number theory from mathematics for application to waveform design for radar, sonar and communications signals. Typical applications are in public key cryptography, image processing, and frequency hopping techniques. The research will examine GOLOMB conjectures A, B and C as found in the scientific literature referenced in the research proposal. The principal investigator expects to prove conjecture A and to give as complete a proof as possible for conjectures B and C. He recently proved conjecture D (there exists a primitive quadratic of trace 1 over every finite field GF ( ) -- a polynominal x -x+g over GF ( ) whose roots are primitive elements of GF ( )) and intends to extend that to a new Conjecture D .
