GALOIS

This program incorporates functions to generate pseudo-random maximum signals for all prime and extension Galois fields q between 2 and 128. The program can display sum tables, product tables, inverses of all elements, reciprocals of all elements, all primitive elements and all primitive polynomials of order n up to a maximum q^n of 16384.

The fields elements in a maximum length sequence may be converted into signal levels to generate a pseudo-random signal. A custom option allows the user complete freedom to define these conversions, while a design option allows the user to implement predetermined conversions that confer on the pseudo-random signal some useful properties for system identification. Conversions are specifically available for the following:

• Suppression of harmonic multiples of 2 when q = 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29 and 31;
• Suppression of harmonic multiples of 2 and 3 when q = 7, 13, 19, 25 and 31;
• Suppression of harmonic multiples of 2, 3 and 5 when q = 31.

GALOIS is made freely available on this website by permission of Professor H. A. Barker of the University of Wales, Swansea, UK. Download the folder at the bottom of the page. Extract the folder out of the zipped file. To run GALOIS, double-click the application file "GALOIS". The program will run on computers with most versions of Windows. It requires a screen area of 1024 by 768 pixels and small fonts.

If you make use of the GALOIS program in your research, you may like to include the following citation in your publication:

• Barker, H. A.: Design of multi-level pseudo-random signals for system identification. In: Godfrey, K. (ed) Perturbation Signals for System Identification. Prentice Hall, Englewood Cliffs, NJ, 1993.