This paper is concerned with a new family of error-correcting codes
based on algebraic curves over finite fields, and list decoding
algorithms for them. The basic goal in the subject of list decoding is
to construct error-correcting codes $C$ over some alphabet $\Sigma$
which have good rate $R$, and at ... more >>>

Algebraic codes that achieve list decoding capacity were recently
constructed by a careful ``folding'' of the Reed-Solomon code. The
``low-degree'' nature of this folding operation was crucial to the list
decoding algorithm. We show how such folding schemes conducive to list
decoding arise out of the Artin-Frobenius automorphism at primes ... more >>>

We give a new construction of algebraic codes which are efficiently list decodable from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired positive constant $\epsilon$. The worst-case list size output by the algorithm is $O(1/\epsilon)$, matching the existential bound for random ... more >>>