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(2
g–2)
g–(
2–2) with
2 being the gonality of
over
Fq, and thus in particular we have that
Keywords Error correcting codes - Algebraic geometric codes - Trellis state complexity - Gonality sequence of curves
The authors were partially supported respectively by the Grants VA02002 (
Junta de Castilla y León
), Proc. 300681/97-6 (CNPq-Brazil) and SB2000-0225 (Secretaria de Estado de Educación y Universidades del Ministerio de Educación, Cultura y Deportes de España)