For any prime-powerq, it is shown that there existq-ary convolutional codes with the equidistance property that every code word is at the same distance from all code words disagreeing in the information digits to be decoded. These codes are called "uniform codes" and it is shown that they can be encoded in a very simple manner. The block codes most similar to uniform codes are the maximal-length codes which also have the equidistance property. It is shown that the error performance of these classes of codes is nearly identical but that the uniform codes have simpler encoding circuits. This latter fact is of importance in space applications, which is the most likely use for these codes.