Systolic solution of linear systems over GF(p) with partial pivoting

Abstract

We propose two systolic architectures for the Gaussian triangularization and the Gauss-Jordan diagonalization of large dense nxn matrices over GF(p), where p is a prime number. The solution of large dense linear systems over GF(p) is the major computational step in various algorithms issued from arithmetic number theory and computer algebra. The two proposed architectures implement the elimination with partial pivoting, although the operation of the array remains purely systolic. The last section is devoted to the design and layout of a CMOS 8 by 8 Gauss-Jordan diagonalization systolic chip over GF(2).