On Codes From Residue Class Ring Generated Finite Ferrero Pairs

Abstract

In the sequel we consider error-correcting codes constructed from the incidence matrix of a BIB-design, which is generated by a finite Ferrero pair based on a residue class ring. Codes from BIB-designs are already known for often having good properties concerning error-correction. Unfortunately many of the considered codes seem to have a lower quality at the first glance. But via the simple trick of omitting a few of the codewords it is possible to highly improve the quality of these codes. This method also simplifies the calculation of the error-correcting properties and does not affect very much the size of the codes. Also other calculations, like encoding and decoding, do not become harder. After an overview of the general method of constructing codes from finite Ferrero pairs we characterize the case of residue class ring generated ones and then we draw our attention on what the resulting codes look like.