Features of digital signal processing algorithms using Galois fields GF(2n+1)
Suleimenov I.E. Vitulyova Y.S. Matrassulova D.K.
October 2023Public Library of Science
PLoS ONE
2023#18Issue 10 October
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.
Text of the article Перейти на текст статьи
National Engineering Academy of the Republic of Kazakhstan, Almaty, Kazakhstan
Almaty University of Power Engineering and Telecommunications Named After Gumarbek Daukeyev, Almaty, Kazakhstan
National Engineering Academy of the Republic of Kazakhstan
Almaty University of Power Engineering and Telecommunications Named After Gumarbek Daukeyev
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026