Quantum codes from algebraic curves with automorphisms

Abstract

Let Χ be an algebraic curve of genus g ≥ 2 defined over a field Fq 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.

Keywords

• algebraic curves
• algebraic-geometry codes
• quantum algebraic codes