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

The original polynomial P(x) of degree 5 defines a codeword size of n=31 bits where 31 = 2⁵-1; the BCH polynomial G(x) of degree 10 defines 10 parity bits such that k = 31 - 10 = 21 to give (n,k) = (31,21).

This BCH (31,21) code can correct at least 2 bit errors, as specified. (See the codewords and matrices)

Model C-182T BCH CODE GENERATOR P(x) = 1011 : P[x] = x3+x+1 1101 : P[x] = x3+x2+1 10011 : P[x] = x4+x+1 11001 : P[x] = x4+x3+1 100101 : P[x] = x5+x2+1 101001 : P[x] = x5+x3+1 101111 : P[x] = x5+x3+x2+x+1 110111 : P[x] = x5+x4+x2+x+1 111011 : P[x] = x5+x4+x3+x+1 111101 : P[x] = x5+x4+x3+x2+1 1000011 : P[x] = x6+x+1 1011011 : P[x] = x6+x4+x3+x+1 1100001 : P[x] = x6+x5+1 1100111 : P[x] = x6+x5+x2+x+1 1101101 : P[x] = x6+x5+x3+x2+1 1110011 : P[x] = x6+x5+x4+x+1    t= 1 2 3 4 5 6 7 8 9 Derivation  | Row Table  | Discussion  | MATLAB

2026-06-14 05:02:45 ADT Last Updated: 2010-02-23	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...