Accession Number : AD0761536

Title :   Multifold Euclidean Geometry Codes,

Corporate Author : HAWAII UNIV HONOLULU DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Lin,Shu

Report Date : 10 OCT 1972

Pagination or Media Count : 67

Abstract : The paper presents a large class of majority-logic decodable cyclic codes whose structure is based on the structural properties of Euclidean geometries and codes that are invariant under the affine group of permutations. One of the basic features of a code in this class is that its null space contains the incidence vectors of specific unions of mu-flats in the Euclidean geometry EG(m,(p sub s)). This class of codes contains many interesting subclasses, among them are the ordinary Euclidean geometry (EG) codes, generalized EG(GEG) codes, and duals of some subclasses of primitive polynomial codes. Moreover, this class of codes has considerable algebraic and geometric structure. Several interesting subclasses of codes have been analyzed. They are proved to be efficient and completely orthogonalizable. Results obtained from this paper include: (1) Characterization of the roots of the generator polynomial of a code in this class; (2) Determination of majority-logic error-correcting capability; (3) Algebraic structure of the codes; (4) Combinatorial expression for the enumeration of parity-check symbols; (5) Proof of the invariant property under the affine group of permutations; (6) The relationships between this class of codes and the other well known classes of majority-logic decodable codes. (Author)

Descriptors :   (*CODING, INVARIANCE), (*DECODING, PERMUTATIONS), POLYNOMIALS, GEOMETRY, SET THEORY, THEOREMS

Subject Categories : Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE