Accession Number : AD0626730

Title :   ON THE WEIGHT STRUCTURE AND SYMMETRY OF BCH CODES.

Descriptive Note : Scientific rept.,

Corporate Author : HAWAII UNIV HONOLULU DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Peterson,W. Wesley

Report Date : 10 JUL 1965

Pagination or Media Count : 30

Abstract : Weight distributions found by digital computation are given for a number of Bose-Chaudhuri-Hocquenghem codes of length (2 to m power)-1 for m as large as ten. The minimum weight was determined in some additional cases which include all non-trivial double, triple, and quadruple error correcting codes by theoretical results and by computer search. In each known case, the true minimum weight meets the Bose-Chaudhuri-Hocquenghem lower bound. It was observed that ja subj = (n + 1 - j)a sub (n + 1 - j) for all BCH codes for which weights were computed, where n is the code length and a sub j the number of code words of weight j. It is shown that a BCH code extended by the addition of an overall parity check is invarient under permutations of the doublytransitive affine group, and the observed equation holds as a consequence of this symmetry. (Author)

Descriptors :   (*CODING, ERRORS), CORRECTIONS, INFORMATION THEORY, WEIGHT, DISTRIBUTION

Subject Categories : Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE