Bounding the Trellis State Complexity of Algebraic Geometric Codes

Abstract. Let C be an algebraic geometric code of dimension k and length n constructed on a curve X over Fq. Let s(C) be the state complexity of C and set w(C) := min{k, n-k}, the Wolf upper bound on s(C). We introduce a numerical function R that depends on the gonality sequence of X and show that s(C) w(C) - R(2g - 2), where g is the genus of X. As a matter of fact, R(2g - 2) g - (2 - 2) with 2 being the gonality of X over Fq, and thus in particular we have that s(C) w(C) - g + 2 - 2.

• Type: Journal
• Year: 2004
• Where: AAECC
• Authors: Carlos Munuera, Fernando Torres
• Keywords: AAECC 2004, Algebraic Geometric Code, Algorithms, State Complexity, Wolf Upper