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Group Actions on Binary Resilient Functions

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

Let G n,t be the subgroup of GL(n,ℤ2) that stabilizes {xℤ2 n:|x|≤t}. We determine G n,t explicitly: For 1≤t≤n−2, G n,t =S n when t is odd and G n,t =〈S n ,Δ〉 when t is even, where S n <GL(n,ℤ2) is the symmetric group of degree n and ΔGL(n,ℤ2) is a particular involution. Let ℛ n,t be the set of all binary t-resilient functions defined on ℤ2 n. We show that the subgroup ℤ2 n⋊(G n,t ∪G n,n−1−t )<AGL(n,ℤ2) acts on ℛ n,t /ℤ2. We determine the representatives and sizes of the conjugacy classes of ℤ2 n⋊S n and ℤ2 n⋊〈S n ,Δ〉. These results allow us to compute the number of orbits of ℛ n,t /ℤ2 under the above group action for (n,t)=(5,1) and (6,2).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wright State University, Dayton, Ohio, 45435, USA

    Xiang-Dong Hou

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  1. Xiang-Dong Hou
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Correspondence to Xiang-Dong Hou.

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Keywords: General linear group, Affine linear group, Resilient function.

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Hou, XD. Group Actions on Binary Resilient Functions. AAECC 14, 97–115 (2003). https://doi.org/10.1007/s00200-003-0125-5

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  • DOI: https://doi.org/10.1007/s00200-003-0125-5

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