On the Upper Bounds of MDS Codes

Abstract

Let $M_q(k)$ be the maximum length of MDS codes with parameters $q,k$. In this paper, the properties of $M_q(k)$ are studied, and some new upper bounds of $M_q(k)$ are obtained. Especially we obtain that $M_q(q-1)\le q+2(q\equiv 4(mod6)),M_q(q-2)\le q+1(q\equiv 4(mod6)),M_q(k)\le q+k-3(q=36(5s+1),s\in N$ and $ k=6,7).

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