The code C is the set of vectors satisfying XH =O. In many information betwen [ and n. Using a slight modification of a applications it is desirable to know, for a given weight w, technique of Lipster [7], we obtain whether C contains any words of weight w, i.e., whether there is a vector of weight w satisfying XH = 0. Again, the best general algorithm known for deciding this requires an exponential search, in this case through all 2k codewords, and a faster algorithm would be highly desirable.
Abstraci-It is shown that for each integer b 2 1 infinitely many optimum cyclic b-burst-correcting codes exist, i.e., codes whose length n, redundancy r, and burst-correcting capability b, satisfy n = 2r-h+1 -1. Some optimum codes for b = 3,4, and 5 are also studied in detail.
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