Summary: This chapter discusses quantum error-correcting codes constructed from algebraic curves. We give an introduction to quantum coding theory including bounds on quantum codes. We describe stabilizer codes which are the quantum analog of classical linear codes and discuss the binary and \(q\)-ary CSS construction. Then we focus on quantum codes from algebraic curves including the projective line, Hermitian curves, and hyperelliptic curves. In addition, we describe the asymptotic behaviors of quantum codes from the Garcia-Stichtenoth tower attaining the Drinfeld-Vlăduţ bound.
For the entire collection see [Zbl 1155.94006].