CODES ASSOCIATED WITH O+(2n, 2r) AND POWER MOMENTS OF KLOOSTERMAN SUMS

摘要

In this paper, we construct three binary linear codes C(SO+(2, q)), C(O+(2, q)), and C(SO+(4, q)), respectively associated with the orthogonal groups SO+(2, q), O+(2, q), and SO+(4, q), with q a power of two. Then we obtain recursive formulas for the power moments of Kloosterman and 2-dimensional Kloosterman sums in terms of the frequencies of weights in the codes. This is done via the Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups.