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Three-weight codes and association schemes. (English) Zbl 0546.94016
Summary: Three-weight projective codes C are considered for which the restriction to C of the Hamming association scheme \(H_ n(q)\) is an association scheme with three classes. Sufficient conditions are established and restrictions on the three weights of C are obtained. It is shown in the binary case that the three-weight subcodes of the shortened second-order Reed-Muller codes provide a large class of examples. Previously known examples were the duals of perfect 3-error-correcting or uniformly packed 2-error-correcting codes.

MSC:
94B25 Combinatorial codes
05B30 Other designs, configurations
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