Title: Quantum codes from algebraic curves with automorphisms
Author(s):

T.Shaska (Science and Engineering Building, Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309 367 Science and Engineering Building, Department of Mathematics and Statistics, Oakland University, Rochester, MI, 48309; University of Maria Curie Sklodovska, Lublin, Poland University of Maria Curie Sklodovska, Lublin, Poland) ,

Let Χ be an algebraic curve of genus g ≥ 2 defined over a field F_q of characteristic p > 0. From Χ, under certain conditions, we can construct an algebraic geometry code C. If the code C is self-orthogonal under the symplectic product then we can construct a quantum code Q, called a QAG-code. In this paper we study the construction of such codes from curves with automorphisms and the relation between the automorphism group of the curve Χ and the codes C and Q.

Key words: algebraic curves, algebraic-geometry codes, quantum algebraic codes
PACS: 03.67.Dd