
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 Randomerrorcorrecting 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 randomerrorcorrectors, although not quite as efficient as the BoseChaudhuriHocquenghem codes. The class of Euclidean geometry codes, as they have been called, contains the class of ReedMuller 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 majoritylogic 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