Quantum codes from two-point Hermitian codes

We explore the background on error-correcting codes, including linear codes and quantum codes from curves. Then we consider the parameters of quantum codes constructed from two-point Hermitian codes

Distance bounds for algebraic geometric codes

Various methods have been used to obtain improvements of the Goppa lower bound for the minimum distance of an algebraic geometric code. The main methods divide into two categories and all but a few of the known bounds are special cases of either the Lundell-McCullough floor bound or the Beelen order bound. The exceptions are recent improvements of the floor bound by Guneri-Stichtenoth-Taskin, and Duursma-Park, and of the order bound by Duursma-Park and Duursma-Kirov. In this paper we provide short proofs for all floor bounds and most order bounds in the setting of the van Lint and Wilson AB method. Moreover, we formulate unifying theorems for order bounds and formulate the DP and DK order bounds as natural but different generalizations of the Feng-Rao bound for one-point codes.Comment: 29 page

AG codes and AG quantum codes from the GGS curve

In this paper, algebraic-geometric (AG) codes associated with the GGS maximal curve are investigated. The Weierstrass semigroup at all $\mathbb F_{q^2}$-rational points of the curve is determined; the Feng-Rao designed minimum distance is computed for infinite families of such codes, as well as the automorphism group. As a result, some linear codes with better relative parameters with respect to one-point Hermitian codes are discovered. Classes of quantum and convolutional codes are provided relying on the constructed AG codes