On Quasi-Cyclic Codes Based on Planar Perfect Difference Sets

For quasi-cyclic codes constructed on the basis of planar difference sets with an odd minimum distance $d$ and rate 1/2, we compute some of the first elements of their weight spectra. The obtained results yield certain parameters of an optimum decoder. We describe a minimum-distance decoding procedure which corrects any $d-2$ errors and can easily be implemented on the basis of a threshold decoder.