65.79 ReedSolomonCode

ReedSolomonCode( n, d )

ReedSolomonCode returns a Reed-Solomon code of length n, designed distance d. This code is a primitive narrow-sense BCH code over the field GF(q), where q=<n>+1. The dimension of an RS code is <n>-<d>+1. According to the Singleton bound (see UpperBoundSingleton) the dimension cannot be greater than this, so the true minimum distance of an RS code is equal to d and the code is maximum distance separable (see IsMDSCode).

    gap> C1 := ReedSolomonCode( 3, 2 );
    a cyclic [3,2,2]1 Reed-Solomon code over GF(4)
    gap> C2 := ReedSolomonCode( 4, 3 );
    a cyclic [4,2,3]2 Reed-Solomon code over GF(5)
    gap> RootsOfCode( C2 );
    [ Z(5), Z(5)^2 ]
    gap> IsMDSCode(C2);
    true 

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