There is no Binary Linear \([66,13,28]\)-Code

Abstract

A binary linear code of length \(n\), dimension \(k\), and minimum distance at least \(d\) is called an \([n,k,d]\)-code. Let \(d(n,k) = \max \{d : \text{there exists an } [n,k,d]\text{-code}\}\). It is currently known by [6] that \(26 \leq d(66,13) \leq 28\). The nonexistence of a linear \([66,13,28]\)-code is proven.