Problems on q-Analogs in Coding Theory

TL;DR

This paper reviews recent research on q-analogs in coding theory, highlights open problems, and proposes initial directions for future work to advance understanding in this area.

Contribution

It summarizes recent developments, compiles 100 open problems, and initiates discussion on potential approaches to solve these challenges.

Findings

Summary of recent research and references

Identification of 100 open problems

Proposed initial directions for research

Abstract

The interest in $q$-analogs of codes and designs has been increased in the last few years as a consequence of their new application in error-correction for random network coding. There are many interesting theoretical, algebraic, and combinatorial coding problems concerning these q-analogs which remained unsolved. The first goal of this paper is to make a short summary of the large amount of research which was done in the area mainly in the last few years and to provide most of the relevant references. The second goal of this paper is to present one hundred open questions and problems for future research, whose solution will advance the knowledge in this area. The third goal of this paper is to present and start some directions in solving some of these problems.