Bitslicing and the Method of Four Russians Over Larger Finite Fields

We present a method of computing with matrices over very small finite fields of size larger than 2. Specifically, we show how the Method of Four Russians can be efficiently adapted to these larger fields, and introduce a row-wise matrix compression scheme that both reduces memory requirements and allows one to vectorize element operations. We also present timings which confirm the efficiency of these methods and exceed the speed of the fastest implementations the authors are aware of. Key words: Finite field, exact linear algebra, matrix multiplication 1