The automorphism groups of Reed-Solomon codes |
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Institution: | Mathematisches Institut, Universität Innsbruck, 6020 Innsbruck, Austria |
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Abstract: | A class of maximum distance separable codes is introduced which includes Reed Solomon codes; extended Reed-Solomon codes, and other cyclic or pseudocyclie MDS codes studied recently. This class of codes, which we call “Cauchy codes” because of the special form of their generator matrices, forms a closed submanifold of dimension 2n - 4 in the k × (n - k)-dimensional algebraic manifold of all MDS codes of length n and dimension k. For every Cauchy code we determine the automorphism group and its underlying permutation group. Far doubly-extended Reed-Solomon codes over GF(q) the permutation group is the semilinear fractional group PΛL(2, q). |
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