Codes associated with O(3,2^r) and power moments of Kloosterman sums with trace one arguments
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We construct a binary linear code C(O(3; q)), associated with the orthogonal group O(3; q). Here q is a power of two. Then we obtain a recursive formula for the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the codes C(O(3; q)) and C(Sp(2; q)). This is done via Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups.
Abstract
We construct a binary linear code C(O(3; q)), associated with the orthogonal group O(3; q). Here q is a power of two. Then we obtain a recursive formula for the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the codes C(O(3; q)) and C(Sp(2; q)). This is done via Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups.
참고문헌 (16)
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