A systematic convolutional encoder of rate (n-1)/n and maximum memory D generates a code of free distance at most V = D + 2 and, at best, a column distance profile (CDP) of [2,3, .. . , D]. A code is memory maximum distance separable if it possesses this CDP. Applied on a communication channel over which packets are transmitted sequentially and which loses (erases) packets randomly, such a code allows the recovery from any pattern of j erasures in the first j n-packet blocks for j <; V, with a delay of exactly j blocks counting from the first non-corrected erasure. This paper addresses the problem of finding the largest V for which a systematic rate (n - 1)/n code over a given field exists, for given n. In particular, constructions for rate (p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> - 1)/p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> and V equal to 3 over GF(p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ) and rate (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-1</sup> -1)/2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-1</sup> and V equal to 4 over GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ) are presented, which provide optimum values of V in their respective cases. A search algorithm is also developed, which produces new codes for V for field sizes 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ≤ 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">14</sup> . Using a complete search version of the algorithm, the maximum value of V, and codes that achieve it, are determined for all code rates ≥ 1/2 and every field size GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ) for m ≤ 5 (and for some rates for m = 6).