Mikael Olofssons Polynomial Service

Irreducible Polynomials over GF(2)

What follows here was once supposed to become a technical report. That report will probably never be written. You can take a look at some of the background material of that non-existing report anyway. The CPU time to find all the polynomials here was at least huge at the time. Therefore I make these polynomials available here for those who might need them.

• Minimum weight table. A table of minimum weight irreducible polynomials over GF(2) for all degrees up to 4000.
• Trinomials. All irreducible polynomials over GF(2) of weight 3 up to at least degree 125.
• Pentanomials. All irreducible polynomials over GF(2) of weight 5 up to degree 50.

The material is found in L^AT_EX format and in Magma form. All information in these files has been found using Magma, a programming language designed for calculations in finite structures, for instance finite fields. For information about Magma, we refer to

• The Magma System for Algebra, Number Theory and Geometry.