Geodesic
Efficient Computing of some Vector Operations over GF(3) and GF(4)
Serdica Journal of Computing, Tome 2 (2008) no. 2, pp. 137-144.

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The problem of efficient computing of the affine vector operations (addition of two vectors and multiplication of a vector by a scalar over GF (q)), and also the weight of a given vector, is important for many problems in coding theory, cryptography, VLSI technology etc. In this paper we propose a new way of representing vectors over GF (3) and GF (4) and we describe an efficient performance of these affine operations. Computing weights of binary vectors is also discussed.
Keywords: Finite Field, Bitwise Representation, Addition of Vectors, Multiplication of a Vector by a Scalar 
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Bouyukliev, Iliya; Bakoev, Valentin. Efficient Computing of some Vector Operations over GF(3) and GF(4). Serdica Journal of Computing, Tome 2 (2008) no. 2, pp. 137-144. http://geodesic.mathdoc.fr/item/SJC_2008_2_2_a2/