Bounding the Trellis State Complexity of Algebraic Geometric Codes

Let [inline-graphic not available: see fulltext] be an algebraic geometric code of dimension k and length n constructed on a curve [inline-graphic not available: see fulltext] over Fq. Let [inline-graphic not available: see fulltext] be the state complexity of [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext] the Wolf upper bound on [inline-graphic not available: see fulltext]. We introduce a numerical function R that depends on the gonality sequence of [inline-graphic not available: see fulltext] and show that [inline-graphic not available: see fulltext] where g is the genus of [inline-graphic not available: see fulltext]. As a matter of fact, R(2g−2)≤g−(γ2−2) with γ2 being the gonality of [inline-graphic not available: see fulltext] over Fq, and thus in particular we have that [inline-graphic not available: see fulltext]