A Goppa-like bound on the trellis state complexity of algebraic geometric codes
<|reference_start|>A Goppa-like bound on the trellis state complexity of algebraic geometric codes: 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.<|reference_end|>
@article{munuera2002a,
    title={A Goppa-like bound on the trellis state complexity of algebraic
  geometric codes},
    author={Carlos Munuera and Fernando Torres},
    journal={arXiv preprint arXiv:math/0212038},
    year={2002},
    archivePrefix={arXiv},
    eprint={math/0212038},
    primaryClass={math.AG cs.IT math.IT}
}