1. Features of digital signal processing algorithms using Galois fields GF(2n+1).
- Author
-
Suleimenov, Ibragim E., Vitulyova, Yelizaveta S., and Matrassulova, Dinara K.
- Subjects
- *
FINITE fields , *DIGITAL signal processing , *ADDITION (Mathematics) , *PRIME numbers , *MULTIPLICATION - Abstract
An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2n+1 to an addition operation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF