Gauss sums for O⁻(2n,q)

Gauss sums for U(2n, q2)

“…Similar sums for other classical groups over a finite field have been considered ( [3]- [7]) and the results for these sums will appear in various places. …”

INFINITE FAMILIES OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF TERNARY KLOOSTERMAN SUMS WITH SQUARE ARGUMENTS ASSOCIATED WITH O-(2n, q)

“…both associated with ρQσ n−3 Q, with respect to the maximal parabolic subgroup Q = Q(2n, q) of the special orthogonal group SO − (2n, q), and express those power moments in terms of the frequencies of weights in each code. Then, thanks to our previous results on the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups O − (2n, q) [4,5], we can express the weight of each codeword in the duals of the codes in terms of Kloosterman sums or squares of Kloosterman sums. Then our formulas will follow immediately from the Pless power moment identity.…”

“…For more details about this section, one is referred to the paper [4] and [5]. Throughout this paper, the following notations will be used: The orthogonal group O − (2n, q) over the field F q is defined as:…”

“…Also, from Section 6 of [4], it is shown that Gauss sum for O − (2n, q), with ψ a nontrivial additive character of F q , is given by: ∑…”

Exponential sums for O-(2n,q) and their applications

“…As the sum in (1.3) vanishes for r = 1, the polynomials involving (1.3) do not appear in that case. For r = 1, similar sums for other classical groups over a finite field had been considered ( [7]- [12], [15], [16]). …”