2008/01/25 by David Joyner, Joyner, David, Amy Ksir +3
Computer Science · Engineering · Mathematics · #11T71 #94B27 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Rings, Modules, and Algebras #graph theory and CDMA systems #math.AG #math.CO #msc:11T71 #msc:94B27
paper · pdf · doi:10.48550/arxiv.0801.4007
11 pages. Appeared in Advances in coding theory and cryptology, (T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko, editors), World Scientific, 2007
arxiv created 2008/01/25 · openalex publication_date 2008/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.