Fractional decoding of algebraic geometry codes over extension fields
<|reference_start|>Fractional decoding of algebraic geometry codes over extension fields: In this paper, we study algebraic geometry codes from curves over $\mathbb{F}_{q^\ell}$ through their virtual projections which are algebraic geometric codes over $\mathbb{F}_q$. We use the virtual projections to provide fractional decoding algorithms for the codes over $\mathbb{F}_{q^\ell}$. Fractional decoding seeks to perform error correction using a smaller fraction of $\mathbb{F}_q$-symbols than a typical decoding algorithm. In one instance, the bound on the number of correctable errors differs from the usual lower bound by the degree of a pole divisor of an annihilator function. In another, we view the virtual projections as interleaved codes to, with high probability, correct more errors than anticipated.<|reference_end|>
@article{camps-moreno2024fractional,
    title={Fractional decoding of algebraic geometry codes over extension fields},
    author={Eduardo Camps-Moreno, Gretchen L. Matthews and Welington Santos},
    journal={arXiv preprint arXiv:2404.07201},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.07201},
    primaryClass={cs.IT math.AG math.IT}
}