ON THE WEIGHT STRUCTURE AND SYMMETRY OF BCH CODES.
HAWAII UNIV HONOLULU DEPT OF ELECTRICAL ENGINEERING
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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