Handbook of Coding Theory
The Newton Polygon of Plane Curves with Many Rational Points
Designs, Codes and Cryptography
Fibre products of Kummer covers and curves with many points
Applicable Algebra in Engineering, Communication and Computing
Effective construction of algebraic geometry codes
IEEE Transactions on Information Theory - Part 1
Construction and decoding of a class of algebraic geometry codes
IEEE Transactions on Information Theory
Kummer Covers with Many Points
Finite Fields and Their Applications
Newton polygons and curve gonalities
Journal of Algebraic Combinatorics: An International Journal
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Baker's theorem is a theorem giving an upper-bound for the genus of a plane curve. It can be obtained by studying the Newton-polygon of the defining equation of the curve. In this paper we give a different proof of Baker's theorem not using Newton-polygon theory, but using elementary methods from the theory of function fields (Theorem 2.4). Also we state a generalization to several variables that can be used if a curve is defined by several bivariate polynomials that all have one variable in common (Theorem 3.3). As a side result, we obtain a partial explicit description of certain Riemann-Roch spaces, which is useful for applications in coding theory. We give several examples and compare the bound on the genus we obtain, with the bound obtained from Castelnuovo's inequality.