About Methods of Vector Addition over Finite Fields Using Extended Vector Registers

We present optimized algorithm for vector addition over finite prime fields using the extended vector registers of modern central processing units (CPU) and the corresponding extended Intel instruction sets SSE, AVX and AVX512. The presented algorithm is based on representation of the elements of the fields using unsigned 8-bit packed integer, thus allowing for computations over prime fields with up to 127 elements. The efficiency of the presented method is demonstrated in an algorithm for calculating the weight distribution of a linear code over the finite field which is known to be an NP-complete problem. An optimized approach for computing the weight of a vector is also given. The experimental results show faster execution times compared to the corresponding algorithms in the Magma and GUAVA package for GAP packages for finite fields larger than 3.