From the preface:
In February 2016, we held a conference on Algebraic Geometry for Coding Theory and Cryptography at the Institute for Pure and Applied Mathematics (IPAM) on the campus of the University of California, Los Angeles. The conference was run in cooperation with the Association for Women in Mathematics (AWM) and was designed in the research collaboration format that underlies many of the conferences whose proceedings appear in the AWM Springer Series. We are pleased to add this volume to the series. The goal of the conference was to bring together researchers working in Algebraic Geometry, Coding Theory, and Cryptography to cross-fertilize the ideas and problems from these areas […]
Six groups of between five and seven people each were formed ahead of the conference to work on interdisciplinary research problems. Group leaders were selected who were willing to design and lead projects, and the rest of the slots were left open so that graduate students, postdoctoral researchers, and junior faculty could apply […] During the conference, a very small number of talks in the mornings gave overviews of the research problems, while the majority of each day was spent in group work to make progress on the problems […] Groups were encouraged to continue their research together after the conference to produce a research article representing their results. In December 2016 five of the six groups submitted papers for peer review, and this volume consists of revised versions of these five papers.
[…] Chapter 1 brings algebraic techniques to bear on the multicast network coding problem. Chapter 2 focuses on error-correcting codes from hypersurfaces in weighted projective space. Chapter 3 uses modular polynomials to improve point-counting algorithms for Jacobians of genus-2 curves, which are important for curve selection in cryptography. Chapter 4 presents several constructions of locally recoverable codes from algebraic curves and surfaces. Chapter 5 proposes variants of the McEliece cryptosystem based on several different constructions of codes.