These are some GAP functions that work on Domains
in general. Their
specific effect on Codes
is explained here.
IsFinite( C )
IsFinite
is an implementation of the GAP domain function
IsFinite
. It returns true for a code C.
gap> IsFinite( RepetitionCode( 1000, GF(11) ) ); true
Size( C )
Size
returns the size of C, the number of elements of the code. If
the code is linear, the size of the code is equal to q^k, where q is
the size of the base field of C and k is the dimension.
gap> Size( RepetitionCode( 1000, GF(11) ) ); 11 gap> Size( NordstromRobinsonCode() ); 256
Field( C )
Field
returns the base field of a code C. Each element of C
consists of elements of this base field. If the base field is F, and
the word length of the code is n, then the codewords are elements of
F^n. If C is a cyclic code, its elements are interpreted as
polynomials with coefficients over F.
gap> C1 := ElementsCode([[0,0,0], [1,0,1], [0,1,0]], GF(4)); a (3,3,1..3)2..3 user defined unrestricted code over GF(4) gap> Field( C1 ); GF(2^2) gap> Field( HammingCode( 3, GF(9) ) ); GF(3^2)
Dimension( C )
Dimension
returns the parameter k of C, the dimension of the code,
or the number of information symbols in each codeword. The dimension is
not defined for non-linear codes; Dimension
then returns an error.
gap> Dimension( NordstromRobinsonCode() ); Error, dimension is only defined for linear codes gap> Dimension( NullCode( 5, GF(5) ) ); 0 gap> C := BCHCode( 15, 4, GF(4) ); a cyclic [15,7,5]4..8 BCH code, delta=5, b=1 over GF(4) gap> Dimension( C ); 7 gap> Size( C ) = Size( Field( C ) ) ^ Dimension( C ); true
Elements( C )
Elements
returns a list of the elements of C. These elements are of
the codeword type (see Codewords). Note that for large codes,
generating the elements may be very time- and memory-consuming. For
generating a specific element or a subset of the elements, use
CodewordNr
(see CodewordNr).
gap> C := ConferenceCode( 5 ); a (5,12,2)1..4 conference code over GF(2) gap> Elements( C ); [ [ 0 0 0 0 0 ], [ 1 1 0 1 0 ], [ 1 1 1 0 0 ], [ 0 1 1 0 1 ], [ 1 0 0 1 1 ], [ 0 0 1 1 1 ], [ 1 0 1 0 1 ], [ 0 1 0 1 1 ], [ 1 0 1 1 0 ], [ 0 1 1 1 0 ], [ 1 1 0 0 1 ], [ 1 1 1 1 1 ] ] gap> CodewordNr( C, [ 1, 2 ] ); [ [ 0 0 0 0 0 ], [ 1 1 0 1 0 ] ]
GAP 3.4.4