A Goppa-like bound on the trellis state complexity of algebraic geometric codes

Details A Goppa-like bound on the trellis state complexity of algebraic geometric codes A Goppa-like bound on the trellis state complexity of algebraic geometric codes

2002-12-03

arxiv.org/abs/math/0212038v1

Mathematics

Algebraic Geometry

LaTeX, 13 pages, IEEE Trans. Inform. Theory: to appear, available at http://www.ime.unicamp.br/~ftorres

Scientific paper

For a linear code $\cC$ of length $n$ and dimension $k$, Wolf noticed that the trellis state complexity $s(\cC)$ of $\cC$ is upper bounded by $w(\cC):=\min(k,n-k)$. In this paper we point out some new lower bounds for $s(\cC)$. In particular, if $\cC$ is an Algebraic Geometric code, then $s(\cC)\geq w(\cC)-(g-a)$, where $g$ is the genus of the underlying curve and $a$ is the abundance of the code.

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