Galois self-orthogonal (SO) codes are generalizations of Euclidean and
Hermitian SO codes. Algebraic geometry (AG) codes are the first known class of
linear codes exceeding the Gilbert-Varshamov bound. Both of them have attracted
much attention for their rich algebraic structures and wide applications in
these years. In this paper, we consider them together and study Galois SO AG
codes. A criterion for an AG code being Galois SO is presented. Based on this
criterion, we construct several new classes of maximum distance separable (MDS)
Galois SO AG codes from projective lines and several new classes of Galois SO
AG codes from projective elliptic curves, hyper-elliptic curves and hermitian
curves. In addition, we give an embedding method that allows us to obtain more
MDS Galois SO codes from known MDS Galois SO AG codes.Comment: 18paper