65.33 InnerDistribution

InnerDistribution( C )

InnerDistribution returns the inner distribution of C. The i^{th} element of the vector contains the average number of elements of C at distance i-1 to an element of C. For linear codes, the inner distribution is equal to the weight distribution (see WeightDistribution).

Suppose w is the inner distribution of C. Then w[1] = 1, because each element of C has exactly one element at distance zero (the element itself). The minimum distance of C is the smallest value d > 0 with w[d+1] neq 0, because a distance between zero and d never occurs. See MinimumDistance.

    gap> InnerDistribution( ConferenceCode(9) );
    [ 1, 0, 0, 0, 63/5, 9/5, 18/5, 0, 9/10, 1/10 ]
    gap> InnerDistribution( RepetitionCode( 7, GF(4) ) );
    [ 1, 0, 0, 0, 0, 0, 0, 3 ] 

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