Features of digital signal processing algorithms using Galois fields GF(2n+1).
basic_science · Level V
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- Record sourced from PubMed, PMID 37878646.
- Also identified by DOI 10.1371/journal.pone.0293294 and PMC identifier 10599577.
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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.
Medical subject headings
- Algorithms
- Signal Processing, Computer-Assisted