  A class of one-dimensional convolutional codes will be presented. They are
all MDS codes, i. e., have the largest distance among all one-dimensional codes
of the same length n and overall constraint length delta. Furthermore, their
extended row distances are computed, and they increase with slope n-delta. In
certain cases of the algebraic parameters, we will also derive parity check
matrices of Vandermonde type for these codes. Finally, cyclicity in the
convolutional sense will be discussed for our class of codes. It will turn out
that they are cyclic if and only if the field element used in the generator
matrix has order n. This can be regarded as a generalization of the block code
case.
