Maximum distance separable (MDS) convolutional codes are defined as the row space over <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F(D)</tex> of totally nonsingular polynomial matrices in the indeterminate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> . These codes may be used to transmit information on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> parallel channels when a temporary or even an infinite break can occur in some of these channels. Their algebraic properties are emphasized, and the relevant parameters are introduced. On this basis two decoding procedures are described. Both procedures correct arbitrarily long error sequences that may occur at the same time in some of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> channels. Some specific constructions of MDS convolutional codes are presented.