Although Kloosterman sums of odd prime powers have been studied extensively, many authors avoid the case where p = 2. This case is important as Kloosterman sums for fields of characteristic 2 have been useful in error-correcting codes and Kloosterman sums over the ring of integers modulo pr have been helpful in studying the spectra of Euclidean graphs. After stating some well-known facts about Kloosterman sums, we evaluate several generalized Kloosterman sums modulo 2^{r}.

*Proceedings of the Thirty-Fourth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 165 (2003), 65–75 . *

**MR2049122 11T24 (11L05)**