65.34 OuterDistribution

OuterDistribution( C )

The function OuterDistribution returns a list of length q^n, where q is the size of the base field of C and n is the word length. The elements of the list consist of an element of (GF(q))^n (this is a codeword type) and the distribution of distances to the code (a list of integers). This table is very large, and for n > 20 it will not fit in the memory of most computers. The function DistancesDistribution (see DistancesDistribution) can be used to calculate one entry of the list.

    gap> C := RepetitionCode( 3, GF(2) );
    a cyclic [3,1,3]1 repetition code over GF(2)
    gap> OD := OuterDistribution(C);
    [ [ [ 0 0 0 ], [ 1, 0, 0, 1 ] ], [ [ 1 1 1 ], [ 1, 0, 0, 1 ] ],
      [ [ 0 0 1 ], [ 0, 1, 1, 0 ] ], [ [ 1 1 0 ], [ 0, 1, 1, 0 ] ],
      [ [ 1 0 0 ], [ 0, 1, 1, 0 ] ], [ [ 0 1 1 ], [ 0, 1, 1, 0 ] ],
      [ [ 0 1 0 ], [ 0, 1, 1, 0 ] ], [ [ 1 0 1 ], [ 0, 1, 1, 0 ] ] ]
    gap> WeightDistribution(C) = OD[1][2];
    true
    gap> DistancesDistribution( C, Codeword("110") ) = OD[4][2];
    true 

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