News
Lecture 4 slides/recording
Written on 05.05.2021 17:29 by Anand Narayanan
Hi All,
The most difficult (algebraic-geometric) part of the course is done!
From here on, the lectures will be elementary, self contained and catered towards computer science applications.
Recoding:
https://www.youtube.com/watch?v=IHOSkTq8O2c
Slides:
https://drive.google.com/file/d/1bRqSbvgYmsVCQZvdFWXMJZO2A2UcTpWU/view?usp=sharing
Our lecture may be the easiest way to get started on Garcia-Stichtenoth towers, all the other expositions target advanced mathematics audiences. The best such sources are
1.) Stichtenoth's book (see course description) and
2.) https://link.springer.com/article/10.1007/BF01884295
For fast computation of Riemann-Roch spaces of curves over finite fields:
1) For plane curves:
https://www.sciencedirect.com/science/article/pii/S0747717184710637
2.) For curves in higher dimensional ambient space:
http://www.staff.uni-oldenburg.de/florian.hess/publications/rr.pdf
3.) For Garcia-Stichtenoth towers:
https://ieeexplore.ieee.org/document/923746
https://ieeexplore.ieee.org/document/945244
For nearly linear time codes beating the Gilbert-Varshamov bound
https://ieeexplore.ieee.org/document/8770116
(there is a free version on arxiv or email me, I can send you the paper for free as an authour).
Decoding:
Shokrollahi-Wasserman algorithm.
https://dl.acm.org/doi/10.1145/276698.276753
-Anand