SOME CODES WHICH ARE INVARIENT UNDER A DOUBLY-TRANSITIVE PERMUTATION GROUP AND THEIR CONNECTION WITH BALANCED INCOMPLETE BLOCK DESIGNS
HAWAII UNIV HONOLULU (MANOA CAMPUS) DEPT OF ELECTRICAL ENGINEERING
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If a binary code is invariant under a doubly-transitive permutation group, then the set of all code words of weight j forms a balanced incomplete block design. Besides the extended normal BCH codes and the extended quadratic residue codes, the Reed-Muller codes are proven to be invariant under a doubly- transitive permutation group. Thus, BIB designs can be derived from these classes of codes. It is shown that if the symbols of the Reed-Muller codes are properly arranged, and if the first digit is omitted, then all Reed-Muller codes are cyclic.