The following is a list of some of the smaller error correcting generator polynomials. There are thousands more.
generator bits bits total hpo2
polynomial in in bits
message checksum
decimal binary
7 111 1 2 3 4
11 1011 4 3 7 8
13 1101 4 3 7 8
19 10011 11 4 15 16
25 11001 11 4 15 16
37 100101 26 5 31 32
41 101001 26 5 31 32
47 101111 26 5 31 32
55 110111 26 5 31 32
59 111011 26 5 31 32
61 111101 26 5 31 32
67 1000011 57 6 63 64
91 1011011 57 6 63 64
97 1100001 57 6 63 64
103 1100111 57 6 63 64
109 1101101 57 6 63 64
115 1110011 57 6 63 64
