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.
Funder
Ministry of Higher Education and Science of the Republic of Kazakhstan
Publisher
Public Library of Science (PLoS)
Reference27 articles.
1. Complexity evaluation of non-binary Galois field LDPC code decoders.;T. Lehnigk-Emden;2010 6th International Symposium on Turbo Codes & Iterative Information ProcessingIEEE,2010
2. New Quantum and LCD Codes over Finite Fields of Even Characteristic;H. Isla;Defence Science Journal,2021
3. RISC-V Galois Field ISA Extension for Non-Binary Error-Correction Codes and Classical and Post-Quantum Cryptography;Y. M. Kuo;IEEE Transactions on Computers,2022
4. Some advantages of non-binary Galois fields for digital signal processing;I. Moldakhan;Indonesian Journal of Electrical Engineering and Computer Science,2021
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