Codes from planar near rings
Peter R. Fuchs, Gerhard Höfer, Günter F. Pilz · IEEE Transactions on Information Theory · 1990
It is well known that error-correcting codes give rise to tactical configurations. Conversely, each such configuration determines four different codes, the codewords being the rows or the columns of the incidence matrix A of the tactical configuration, or the linear hulls generated by the rows or the columns of A. These codes, in particular if the tactical configuration is a block design, are investigated. Several of these codes turn out to be 'almost perfect'. The special case in which the balanced incomplete block designs are constructed from planar near rings is also investigated. Special classes of planar near rings (the 'circular' ones) that might be especially useful (see J.R. Clay, 1987 and 1988) are investigated.>