Sequences, Bent Functions and Jacobsthal Sums
نویسندگان
چکیده
The p-ary function f(x) mapping GF(p) to GF(p) and given by f(x) = Tr4k ( ax + bx ) with a, b ∈ GF(p) and d = p + p − p + 1 is studied with the respect to its exponential sum. In the case when either a (p+1) 6= b +1 or a = b with b 6= 0, this sum is shown to be three-valued and the values are determined. For the remaining cases, the value of the exponential sum is expressed using Jacobsthal sums of order p + 1. Finding the values and the distribution of those sums is a long-lasting open problem.
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تاریخ انتشار 2010