Title: Cayley codes with few short generators
Could we have an error correcting code which is of constant rate, constant distance and yet is very symmetric (i.e. the dual code is defined by a few short generators and their orbits under a certain group.)?
Achieving any two of the mentioned three requirements is possible using previous results.
The main question is whether all three requirements could hold simultaneously. In this work we construct a code that is close to achieve this three-folded goal.
Joint work with Avi Wigderson