Document detail
ID
oai:arXiv.org:2404.07201
Topic
Computer Science - Information The... Mathematics - Algebraic GeometryAuthor
Camps-Moreno, Eduardo Matthews, Gretchen L. Santos, WelingtonCategory
Computer Science
Year
2024
listing date
4/17/2024
Keywords
geometry fractional algebraicAbstract
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.
Camps-Moreno, Eduardo,Matthews, Gretchen L.,Santos, Welington, 2024, Fractional decoding of algebraic geometry codes over extension fields
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