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Diskr. Mat., 2018, Volume 30, Issue 3, Pages 77–87 (Mi dm1495)  

On affine classification of permutations on the space $GF(2)^3$

F. M. Malyshev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We give an elementary proof that by multiplication on left and right by affine permutations $A,B\in AGL(3,2)$ each permutation $\pi:GF(2)^3\rightarrow GF(2)^3$ may be reduced to one of the 4 permutations for which the $3\times3$-matrices consisting of the coefficients of quadratic terms of coordinate functions have as an invariant the rank, which is either 3, or 2, or 1, or 0, respectively. For comparison, we evaluate the number of classes of affine equivalence by the Pólya enumerative theory.

Keywords: permutation, affine transformation, Pólya theory, de Brouijn's theorem

DOI: https://doi.org/10.4213/dm1495

Full text: PDF file (534 kB)
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English version:
Discrete Mathematics and Applications, 2019, 29:6, 363–371

Bibliographic databases:

UDC: 512.542.74
Received: 09.01.2018

Citation: F. M. Malyshev, “On affine classification of permutations on the space $GF(2)^3$”, Diskr. Mat., 30:3 (2018), 77–87; Discrete Math. Appl., 29:6 (2019), 363–371

Citation in format AMSBIB
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