Bounding the Trellis State Complexity of Algebraic Geometric Codes

Abstract.Let be an algebraic geometric code of dimension k and length n constructed on a curve over Fq. Let be the state complexity of and the Wolf upper bound on . We introduce a numerical function R that depends on the gonality sequence of and show that where g is the genus of . As a matter of fact, R(2g−2)≤g−(γ2−2) with γ2 being the gonality of over Fq, and thus in particular we have that

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