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Features of digital signal processing algorithms using Galois fields GF(2(n)+1)

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 = 2(n)+1. For such numbers, it is possible to implement...

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Detalles Bibliográficos
Autores principales: Suleimenov, Ibragim E., Vitulyova, Yelizaveta S., Matrassulova, Dinara K.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10599577/
https://www.ncbi.nlm.nih.gov/pubmed/37878646
http://dx.doi.org/10.1371/journal.pone.0293294
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author Suleimenov, Ibragim E.
Vitulyova, Yelizaveta S.
Matrassulova, Dinara K.
author_facet Suleimenov, Ibragim E.
Vitulyova, Yelizaveta S.
Matrassulova, Dinara K.
author_sort Suleimenov, Ibragim E.
collection PubMed
description 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 = 2(n)+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 = 2(n)+1 to an addition operation.
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spelling pubmed-105995772023-10-26 Features of digital signal processing algorithms using Galois fields GF(2(n)+1) Suleimenov, Ibragim E. Vitulyova, Yelizaveta S. Matrassulova, Dinara K. PLoS One Research Article 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 = 2(n)+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 = 2(n)+1 to an addition operation. Public Library of Science 2023-10-25 /pmc/articles/PMC10599577/ /pubmed/37878646 http://dx.doi.org/10.1371/journal.pone.0293294 Text en © 2023 Suleimenov et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Suleimenov, Ibragim E.
Vitulyova, Yelizaveta S.
Matrassulova, Dinara K.
Features of digital signal processing algorithms using Galois fields GF(2(n)+1)
title Features of digital signal processing algorithms using Galois fields GF(2(n)+1)
title_full Features of digital signal processing algorithms using Galois fields GF(2(n)+1)
title_fullStr Features of digital signal processing algorithms using Galois fields GF(2(n)+1)
title_full_unstemmed Features of digital signal processing algorithms using Galois fields GF(2(n)+1)
title_short Features of digital signal processing algorithms using Galois fields GF(2(n)+1)
title_sort features of digital signal processing algorithms using galois fields gf(2(n)+1)
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10599577/
https://www.ncbi.nlm.nih.gov/pubmed/37878646
http://dx.doi.org/10.1371/journal.pone.0293294
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