Automorphism groups of generalized Reed-Solomon codes

Details Automorphism groups of generalized Reed-Solomon codes Automorphism groups of generalized Reed-Solomon codes

2008-01-25

arxiv.org/abs/0801.4007v1

Mathematics

Algebraic Geometry

11 pages. Appeared in Advances in coding theory and cryptology, (T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko, editors),

Scientific paper

We look at AG codes associated to the projective line, re-examining the problem of determining their automorphism groups (originally investigated by Duer in 1987 using combinatorial techniques) using recent methods from algebraic geometry. We (re)classify those finite groups that can arise as the automorphism group of an AG code for the projective line and give an explicit description of how these groups appear. We also give examples of generalized Reed-Solomon codes with large automorphism groups G, such as G=PSL(2,q), and explicitly describe their G-module structure.

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