Accession Number : AD0654675

Title :   EUCLIDEAN GEOMETRY CYCLIC CODES,

Corporate Author : HAWAII UNIV HONOLULU DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Weldon,E. J. , Jr

Report Date : 15 FEB 1967

Pagination or Media Count : 22

Abstract : A class of Random-error-correcting cyclic codes is defined and investigated. It is shown that a suitable choice of generator polynomial guarantees that the polynomials corresponding to all subspaces of a given dimensionality in a particular Euclidean geometry are in the null space of the code. These subspaces (flats) are useful in deriving a seemingly tight lower bound on the minimum distance of the codes. This bound shows that for practical values of code length the codes are rather efficient random-error-correctors, although not quite as efficient as the Bose-Chaudhuri-Hocquenghem codes. The class of Euclidean geometry codes, as they have been called, contains the class of Reed-Muller codes. It is shown that with a slight modification the decoding algorithm for these latter codes can be applied to the Euclidean geometry codes. This algorithm, referred to in the literature both as the Reed Algorithm and majority-logic decoding, can be implemented in a surprisingly simple manner. (Author)

Descriptors :   (*CODING, ERRORS), INFORMATION THEORY, GEOMETRY, POLYNOMIALS, RANDOM VARIABLES, ALGORITHMS, DECODING, MATHEMATICAL ANALYSIS

Subject Categories : Theoretical Mathematics
      Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE