Non-linear Cyclic Codes that Attain the Gilbert-Varshamov Bound

TL;DR

This paper demonstrates the existence of non-linear binary cyclic codes that reach the theoretical maximum size predicted by the Gilbert-Varshamov bound, advancing coding theory.

Contribution

It proves the existence of non-linear cyclic codes that achieve the Gilbert-Varshamov bound, a significant theoretical milestone.

Findings

Existence of non-linear cyclic codes reaching the Gilbert-Varshamov bound

Advancement in understanding the limits of cyclic code constructions

Theoretical proof without explicit code construction

Abstract

We prove that there exist non-linear binary cyclic codes that attain the Gilbert-Varshamov bound.