Abstract
Using the switching method, some classification is pointed out of STS(n) of order n = 2r −1, r > 3, and small rank rn (different by 2 from the rank of the Hamming code of length n), embedded into perfect binary codes of length n and the same rank. The lower and upper bounds on the number of such different STSs are provided.Description of the class of STS(n)s of rank rn, which are not embedded into the perfect binary codes of length n and the same rank, and the lower bound on the number of these different systems are given. It is proved that each STS(n) of rank rn − 1 is embedded into a Vasil’ev code of length n and the same rank.
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