Ping-Zhi Yuan

MDS codes containing a fixed subcode over finite field extensions

Let $2\le k\le n$ and let $U\le\mathbb{F}_q^n$ be a fixed $(k-1)$-dimensional linear code. We study the $[n,k]$ maximum distance separable (MDS) codes over finite extensions of $\mathbb{F}_q$ that contain the scalar extension of $U$. Our approach constructs an auxiliary linear code from \(U\). Its full-weight words cha...