Fermat primes

Fermat primes

Geometry

Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018

A regular n‐gon inscribed in the unit circle can be constructed by straightedge and compass alone if and only if n has the form n = 2ℓp1p2…pk, where ℓ is a nonnegative integer and {pi} are distinct Fermat primes (primes of the form 22m+1 $ 2^{{2^{m} }} + 1 $ ). The only known Fermat primes are for 3, 5, 17, 257, and 65537, corresponding to m = 1, 2, 3, 4. Thus, regular n‐gons can be constructed with this many sides n=3,4,5,6,8,10,12,15,16,17,20,24,…,257,… $ n = 3,4, \, 5, \, 6, \, 8, \, 10, \, 12, \, 15, \, 16, \, 17, \, 20, \, 24, \ldots , \, 257, \ldots $

An erasure-based scheme for reduction of PAPR in spatial multiplexing MIMO-OFDM using Reed-Solomon codes over GF(2¹⁶ + 1)

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Journal Information

Published in International Journal of Electronics, 2018

Mohammad Reza Motazedi, Reza Dianat

In this paper, we propose a new erasure-based scheme using non-systematic RS encoding over GF() (Dianat & Marvasti, 2005) (in which is a Fermat prime number) for joint PAPR reduction and error correction in spatial multiplexing MIMO-OFDM. Moreover, the proposed scheme is much less complex compared to Fischer’s scheme. The technique is also applicable to RS codes over binary extended fields.

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An erasure-based scheme for reduction of PAPR in spatial multiplexing MIMO-OFDM using Reed-Solomon codes over GF(216 + 1)

An erasure-based scheme for reduction of PAPR in spatial multiplexing MIMO-OFDM using Reed-Solomon codes over GF(2¹⁶ + 1)