New codes from old; a new geometric construction (Q5937137)

Let \(C\) be a binary linear \((N,k,d)\) code of minimum distance \(d\) at least 4. Let \(n+ 1= N-k\). Then a basis for \(C^\perp\) forms an \((n+1)\times N\) matrix whose columns form a set of \(N\) triply noncollinear points in \(PG(n,2)\) that is called a cap. The authors provide a new construction for codes via this geometric correspondence whereby they increase the dimension \(k\) of the old code by a factor greater than 2 while increasing the length \(N\) by a factor less than 2. Some applications of their technique are also given.