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A systematic convolutional encoder of rate $(n-1)/n$ and maximum degree $D$generates a code of free distance at most ${\cal D} = D+2$ and, at best, acolumn distance profile (CDP) of $[2,3,\ldots,{\cal D}]$. A code is\emph{Maximum Distance Separable} (MDS) if it possesses this CDP. Applied on acommunication channel over which packets are transmitted sequentially and whichloses (erases) packets randomly, such a code allows the recovery from anypattern of $j$ erasures in the first $j$ $n$-packet blocks for $j<{\cal D}$,with a delay of at most $j$ blocks counting from the first erasure. This paperaddresses the problem of finding the largest ${\cal D}$ for which a systematicrate $(n-1)/n$ code over $GF(2^m)$ exists, for given $n$ and $m$. Inparticular, constructions for rates $(2^m-1)/2^m$ and $(2^{m-1}-1)/2^{m-1}$ arepresented which provide optimum values of ${\cal D}$ equal to 3 and 4,respectively. A search algorithm is also developed, which produces new codesfor ${\cal D}$ for field sizes $2^m \leq 2^{14}$. Using a complete searchversion of the algorithm, the maximum value of ${\cal D}$, and codes thatachieve it, are determined for all code rates $\geq 1/2$ and every field size$GF(2^m)$ for $m\leq 5$ (and for some rates for $m=6$).

Rate $(n-1)/n$ Systematic MDS Convolutional Codes over $GF(2^m)$