Secant Spaces and Cliffordʹs Theorem over Finite Fields

We present here a combinatorial approach to special divisors and secant divisors on curves over finite fields based on their relations with error-correcting codes. Applying to linear systems on curves over finite fields numerous coding theory bounds one gets a lot of bounds on their dimensions. This approach works for curves with many rational points, which leads, for example, to certain ameliorations of Clifford’s theorem for such curves.