### Abstract

We study the cycle structure of those permutations of the finite field F_{qn} of the form L(x) = ∑ i=0 n-1a_{i}x^{qi} where each a_{i} ε{lunate} F_{q}. For such a permutation, the problem of finding its cycle decomposition of F_{qn} can be reduced to finding its cycle decomposition on certain T-invariant subspaces of F_{qn}, where T is the operator defined by T : x → x^{q}. If L_{1}(x) and L_{2}(x)M are in the above form, we say that L_{1}(x) and L_{2}(x) are equivalent if L_{1}(x) and L_{2}(x) induce the same cycle decomposition of F_{qn}, and we say they are strongly equivalent if they induce the same cycle decomposition in every T-invariant subspace of F_{qn}. We show that these notions are not the same, and we give characterizing theorems for each.

Original language | English (US) |
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Pages (from-to) | 63-82 |

Number of pages | 20 |

Journal | Linear Algebra and Its Applications |

Volume | 108 |

Issue number | C |

DOIs | |

State | Published - Sep 1988 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

*Linear Algebra and Its Applications*,

*108*(C), 63-82. https://doi.org/10.1016/0024-3795(88)90179-6