Shortened Finite Geometry Codes
Shu Lin · 1972
In this correspondence two results on finite analytic-geometry codes are presented. First, it is shown that an Euclidean-geometry (EC) code is actually a shortened projective-geometry (PG) code. Next, a method is presented to obtain majority-logic decodable codes by shortening EG codes and 2-fold EG codes. Combinatorial expressions for the number of parity-check symbols of shortened EG codes are derived. The reader is assumed to be familiar with some fundamentals of finite analytic geometries and the works on finite-geometry codes in (I )- (6). For simplicity, we only consider binary codes. All the results in this paper can be generalized to codes over G&J) (where p is a prime integer) in a straightforward manner.