StandardArray( C )
StandardArray returns the standard array of a code C. This is a
matrix with elements of the codeword type. It has q^r rows and q^k
columns, where q is the size of the base field of C, r is the
redundancy of C, and k is the dimension of C. The first row
contains all the elements of C. Each other row contains words that do
not belong to the code, with in the first column their syndrome vector
(see Syndrome).
A non-linear code does not have a standard array. StandardArray then
returns an error.
Note that calculating a standard array can be very time- and memory- consuming.
gap> StandardArray(RepetitionCode(3,GF(3)));
[ [ [ 0 0 0 ], [ 1 1 1 ], [ 2 2 2 ] ],
[ [ 0 0 1 ], [ 1 1 2 ], [ 2 2 0 ] ],
[ [ 0 0 2 ], [ 1 1 0 ], [ 2 2 1 ] ],
[ [ 0 1 0 ], [ 1 2 1 ], [ 2 0 2 ] ],
[ [ 0 2 0 ], [ 1 0 1 ], [ 2 1 2 ] ],
[ [ 1 0 0 ], [ 2 1 1 ], [ 0 2 2 ] ],
[ [ 1 2 0 ], [ 2 0 1 ], [ 0 1 2 ] ],
[ [ 2 0 0 ], [ 0 1 1 ], [ 1 2 2 ] ],
[ [ 2 1 0 ], [ 0 2 1 ], [ 1 0 2 ] ] ]
GAP 3.4.4