Constructions for a 32-word binary code of length 12 and minimum distance 5 were given by Nadler in 1962 and van Lint in 1972. These codes are not equivalent as their distance distributions are not the same. That their extended codes of length 13 are equivalent is proved. It is shown that up to a permutation of the coordinates, there is an essentially unique way to construct the extended code. This unique extended code contains only two inequivalent punctured codes of length 12.

A new infinite class of cyclic codes is studied. Codes of this class can be decoded in a step-by-step manner, using` majority logic. Some previously known codes fall in this class, and thus admit simpler decoding procedures. As random error-correcting codes, the codes are nearly as powerful as the Bose-Chaudhuri codes.

A subclass of cyclic codes of composite block lengthn=n' \cdot n", withn'andn"relatively prime, is studied. It is shown how, under certain conditions, these codes may be factorized into subcodes of block lengthn'andn"and how they are related to codes of block lengthn'orn", over extension fields of the base field. The problem is, in a sense, the converse of the one considered by Burton and Weldon, [5] and some of our codes are subcodes of their product codes. The factorization property gives better insight into the structure of various codes and allows, in particular, to obtain new lower bounds on their minimum weight, hence improving in many cases on the Bose-Chaudhuri bound.