Algebraic Theory of Codes 2

Abstract
The resultant is applied to the problem of weights in cyclic codes. The binary code arising from the projective plane of order 10 (if it exists) is examined. T-design decoding is discussed in general, and the special case of the (48, 24) binary extended quadratic residue code is worked out in detail. The (60,30) ternary extended quadratic residue code is proved to yield new 5- designs. Miscellaneous results include study of the question whether Steiner triple systems support linear codes.

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