Construction of shortened geometric codes as Shown here results in 1-step majority-logic deeodable codes. The shortened codes retain the error-correction ability of the parent codes and the decoders for the shortened codes are much simpler than for the parent code. A table of shortened codes is given.
In this correspondence additional results on majority-logic decoding of product codes are presented. If one of the component codes is decodable using Rudolph's nonorthogonal algorithm, and the other using Reed-Massey'sL-step orthogonalization, then the resulting product code is majority-logic decodable inLsteps, where nonorthogonal checks are used in the first step and orthogonal checks in the remaining steps. If the component codes are both decodable using Rudolph's algorithm, the product code is majority-logic decodable using the same procedure.