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may 2013 Fast vector arithmetic over $\mathbb{F}_3$
K. Coolsaet
Bull. Belg. Math. Soc. Simon Stevin 20(2): 329-344 (may 2013). DOI: 10.36045/bbms/1369316548

Abstract

We show how binary machine instructions can be used to implement fast vector operations over the finite field $\mathbb{F}_3$. Apart from the standard operations of addition, subtraction and dot product, we also consider combined addition and subtraction, weight, Hamming distance, and iteration over all vectors of a given length. Tests show that our implementation can be as much as 10 times faster than the standard method of using modular arithmetic on arrays of bytes. For computing the Hamming distance even a factor of 33 can sometimes be reached, provided a recent CPU is used.

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K. Coolsaet. "Fast vector arithmetic over $\mathbb{F}_3$." Bull. Belg. Math. Soc. Simon Stevin 20 (2) 329 - 344, may 2013. https://doi.org/10.36045/bbms/1369316548

Information

Published: may 2013
First available in Project Euclid: 23 May 2013

zbMATH: 1277.65121
MathSciNet: MR3082768
Digital Object Identifier: 10.36045/bbms/1369316548

Subjects:
Primary: 12-04 , 12E30 , 65Y04

Keywords: 64-bit operations , dot product , Fast vector arithmetic , GF(3) , Hamming distance

Rights: Copyright © 2013 The Belgian Mathematical Society

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Vol.20 • No. 2 • may 2013
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