Capacity-achieving codes: a review on double transitivity
Information Theory
2020-10-30 v1 math.IT
Abstract
Recently it was proved that if a linear code is invariant under the action of a doubly transitive permutation group, it achieves the capacity of erasure channel. Therefore, it is of sufficient interest to classify all codes, invariant under such permutation groups. We take a step in this direction and give a review of all suitable groups and the known results on codes invariant under these groups. It turns out that there are capacity-achieving families of algebraic geometric codes.
Keywords
Cite
@article{arxiv.2010.15453,
title = {Capacity-achieving codes: a review on double transitivity},
author = {Kirill Ivanov and Rüdiger L. Urbanke},
journal= {arXiv preprint arXiv:2010.15453},
year = {2020}
}