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:

1965-07-10

Pagination or Media Count:

30.0

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 - ja 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