Construction of Explicit Irreducible Polynomials over F2 in Cluster Computational Environment

Abstract

This paper describes a method for constructing families of explicit irreducible polynomials over F2. The proposed method allows construction of explicit polynomials of higher degree over F2 from a given sequence of primitive polynomials. A computational algorithm has been developed and implemented on base of this method. The program is realized in the most effective way possible in cluster computational environment. Allocation and distribution of memory resources have been implemented in a careful manner, since data size increases drastically with increasing of the amount of computations required. Program paralleling is performed using data paralleling, i.e. data is distributing among all processors, which ran the same program and each of which builds the subsequent irreducible polynomial, and finally a sequence of all the irreducible polynomials in explicit form is obtained. Moreover, the program also searches for the polynomial with the lowest possible weight among of all the polynomials of the same degree.