Log/antilog tables for GF(256) multiplication (polynomial basis)

When working with Reed-Solomon codes, log/antilog tables are helpful to calculate Galois field (finite field) products by hand.

This PDF contains log/antilog tables for all 30 irreducible polynomials in GF(256). This all polynomial bases for GF(256). 16 of these polynomials are primitive. Of special note, the primitive polynomials 0x11D and 0x187 are most commonly used in Reed-Solomon codes. The non-primitive polynomial 0x11B is used by the AES encryption algorithm and the Intel CPU instruction GF2P8MULB. Non-primitive, irreducible polynomials can be used for Reed-Solomon codes, but some software does not support non-primitive polynomials (such as MATLAB/Octave and Phil Karn’s libfec).


Primitive elements in GF(256) (polynomial basis)

A Reed-Solomon code generator polynomial requires selection of a primitive element of GF(256). The 128 primitive elements of GF(256) for a polynomial basis are listed in the following document.