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Electronic Colloquium on Computational Complexity

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Reports tagged with Algebraic algorithms:
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 >>>

TR21-162 | 14th November 2021
Vishwas Bhargava, Sumanta Ghosh, Mrinal Kumar, Chandra Kanta Mohapatra

Fast, Algebraic Multivariate Multipoint Evaluation in Small Characteristic and Applications

Revisions: 3

Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. Besides being a natural and fundamental question in computer algebra on its own, fast algorithms for this problem is also closely related to fast algorithms for other natural ... more >>>

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