Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

Reports tagged with Class field theory:
TR09-001 | 26th November 2008
Venkatesan Guruswami

Artin automorphisms, Cyclotomic function fields, and Folded list-decodable codes

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 >>>

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 >>>

ISSN 1433-8092 | Imprint