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Jong Yoon Hyun; Lee, Yoonjin
IEEE transactions on information theory, 01/2019, Volume: 65, Issue: 1Journal Article
A Formula Omitted-ary function Formula Omitted in Formula Omitted variables is an Formula Omitted- form if Formula Omitted for any nonzero Formula Omitted in Formula Omitted and Formula Omitted in Formula Omitted. Let Formula Omitted be a positive even integer, Formula Omitted an odd prime, and Formula Omitted an element of Formula Omitted provided that Formula Omitted if Formula Omitted. Let Formula Omitted be a Formula Omitted-ary bent function in Formula Omitted variables of Formula Omitted-form with Formula Omitted and Formula Omitted, and let Formula Omitted. We denote by Formula Omitted the Cayley graph Formula Omitted. Our main results are as follows: 1) if there is weakly regular Formula Omitted-ary bent Formula Omitted which is not regular, then Formula Omitted is 2; 2) if Formula Omitted, then Formula Omitted is weakly regular Formula Omitted-ary bent if and only if the Cayley graph Formula Omitted is strongly regular; 3) if Formula Omitted, then Formula Omitted is regular Formula Omitted-ary bent if and only if the Cayley graph Formula Omitted is strongly regular; 4) Formula Omitted can be replaced by Formula Omitted in 2) and 3); and 5) amorphic association schemes are derived by using 2) and 3). We prove our main results by computing at most four distinct restricted eigenvalues of Formula Omitted.
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