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Features of digital signal processing algorithms using Galois fields GF(2n+1)
Ibragim E Suleimenov1, Yelizaveta S Vitulyova2, Dinara K Matrassulova2
1National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan.
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.
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