65.111 UpperBoundSingleton

UpperBoundSingleton( n, d, q )

UpperBoundSingleton returns the Singleton bound for a code of length n, minimum distance d over a field of size q. This bound is based on the shortening of codes. By shortening an (n, M, d) code d-1 times, an (n-d+1,M,1) code results, with M leq q^{n-d+1} (see ShortenedCode). Thus M leq q^n-d+1

Codes that meet this bound are called maximum distance separable (see IsMDSCode).

    gap> UpperBoundSingleton(4, 3, 5);
    25
    gap> C := ReedSolomonCode(4,3);; Size(C);
    25
    gap> IsMDSCode(C);
    true 

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