UNB ECE4253 Digital Communications
Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

Polynomial GF(2) Factoring Tool

Binary values expressed as polynomials in GF(2) can readily be manipulated using the rules of GF(2) arithmetic.

This online tool completely factors any GF(2) polynomial up to x32 (33 bits long). Binary and decimal equivalents are shown for reference. Note that irreducible polynomials expressed in decimal form do not necessarily correspond to prime positive integers.

Table of Factors     Table of Irreducible P(x)     Factors of xn+1


Polynomial:

x31+1

(10000000000000000000000000000001)

(2147483649)

Factors:

(x+1) (x5+x2+1) (x5+x3+1) (x5+x3+x2+x+1) (x5+x4+x2+x+1) (x5+x4+x3+x+1) (x5+x4+x3+x2+1)

(11)(100101)(101001)(101111)(110111)(111011)(111101)

(3)(37)(41)(47)(55)(59)(61)

Binary Value: Discussion

Predefined: [ x7+1 ] [ x15+1 ] [ x31+1 ] [ CRC-32(IEEE) ] [ CRC-16(ANSI) ] [ CRC-16(CCITT) ] [ CRC-12 ] [ AES ]

2024-07-14 17:45:57 ADT
Last Updated: 2016-01-17
Richard Tervo [ tervo@unb.ca ] Back to the course homepage...