# 65.85 CyclicCodes

`CyclicCodes( n, F )`

`CyclicCodes` returns a list of all cyclic codes of length n over F. It constructs all possible generator polynomials from the factors of x^n-1. Each combination of these factors yields a generator polynomial after multiplication.

`NrCyclicCodes( n, F )`

The function `NrCyclicCodes` calculates the number of cyclic codes of length n over field F.

```    gap> NrCyclicCodes( 23, GF(2) );
8
gap> codelist := CyclicCodes( 23, GF(2) );
[ a cyclic [23,23,1]0 enumerated code over GF(2),
a cyclic [23,22,1..2]1 enumerated code over GF(2),
a cyclic [23,11,1..8]4..7 enumerated code over GF(2),
a cyclic [23,0,23]23 enumerated code over GF(2),
a cyclic [23,11,1..8]4..7 enumerated code over GF(2),
a cyclic [23,12,1..7]3 enumerated code over GF(2),
a cyclic [23,1,23]11 enumerated code over GF(2),
a cyclic [23,12,1..7]3 enumerated code over GF(2) ]
gap> BinaryGolayCode() in codelist;
true
gap> RepetitionCode( 23, GF(2) ) in codelist;
true
gap> CordaroWagnerCode( 23 ) in codelist;
false    # This code is not cyclic ```

GAP 3.4.4
April 1997