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On cyclic MDS codes of length q over GF(q) (Corresp.)

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2 Author(s)

It is shown that a cyclic codeCof lengthqover GF(q)is the maximum distance separable if and only if either1) qis a prime, in which caseCis equivalent, up to a coordinate permutation, to an extended Reed-Solomon code, or2) Cis a trivial code of dimensionk in {1, q - 1, q }. Hence there exists a nontrivial cyclic extended Reed-Solomon code of lengthqover GF(q)if and only ifqis a prime.

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Information Theory, IEEE Transactions on  (Volume:32 ,  Issue: 2 )