Abstract
The present paper contains the complete characterization of all the subschemes of the Hamming scheme H(n, 2). The characterization problem for these subschemes is closely related to the study of the lattice of overgroups of the exponentiation S 2 ↑ S n in the symmetric group \({S_{{2^n}}}\). For this reason the results of the paper can be used in the study of symmetry in algebraic code s, and in the classification of Boolean functions. Some examples of subschemes having two classes for even n were indicated in [4]. All subschemes of H(n, 2) for n ≤ 16 have been classified by computer. A synopsis of these results on enumeration can be found in [5]. An analysis of them led us to a conjecture that the number of subschemes becomes stable when n is sufficiently large. The validity of this conjecture follows from the list of the subschemes of H(n, 2) presented below.
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References
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© 1994 Springer Science+Business Media Dordrecht
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Muzichuk, M.E. (1994). The Subschemes of the Hamming Scheme. In: Faradžev, I.A., Ivanov, A.A., Klin, M.H., Woldar, A.J. (eds) Investigations in Algebraic Theory of Combinatorial Objects. Mathematics and Its Applications, vol 84. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1972-8_4
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DOI: https://doi.org/10.1007/978-94-017-1972-8_4
Publisher Name: Springer, Dordrecht
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