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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > FUNCTION FIELDS:
Reports tagged with Function fields:
TR12-146 | 7th November 2012
Venkatesan Guruswami, Chaoping Xing

List decoding Reed-Solomon, Algebraic-Geometric, and Gabidulin subcodes up to the Singleton bound

We consider Reed-Solomon (RS) codes whose evaluation points belong to a subfield, and give a linear-algebraic list decoding algorithm that can correct a fraction of errors approaching the code distance, while pinning down the candidate messages to a well-structured affine space of dimension a constant factor smaller than the code ... more >>>


TR13-046 | 27th March 2013
Venkatesan Guruswami, Chaoping Xing

Optimal rate list decoding of folded algebraic-geometric codes over constant-sized alphabets

We construct a new list-decodable family of asymptotically good algebraic-geometric (AG) codes over fixed alphabets. The function fields underlying these codes are constructed using class field theory, specifically Drinfeld modules of rank $1$, and designed to have an automorphism of large order that is used to ``fold" the AG code. ... more >>>




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