65.117 UpperBound

UpperBound( n, d, q )

UpperBound returns the best known upper bound A(<n>,<d>) for the size of a code of length n, minimum distance d over a field of size q. The function UpperBound first checks for trivial cases (like <d>=1 or <n>=<d>) and if the value is in the built-in table. Then it calculates the minimum value of the upper bound using the methods of Singleton (see UpperBoundSingleton), Hamming (see UpperBoundHamming), Johnson (see UpperBoundJohnson), Plotkin (see UpperBoundPlotkin) and Elias (see UpperBoundElias). If the code is binary, A(<n>, 2*l-1) = A(<n>+1, 2*l), so the UpperBound takes the minimum of the values obtained from all methods for the parameters (<n>, 2*l-1) and (<n>+1, 2*l).

    gap> UpperBound( 10, 3, 2 );
    85
    gap> UpperBound( 25, 9, 8 );
    1211778792827540 

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