  We analyze the Time-Tagged Event (TTE) data from observations of gamma ray
bursts (GRBs) and soft gamma repeaters (SGRs) by the Burst and Transient Source
Experiment (BATSE). These data provide the best available time resolution for
GRBs and SGRs. We have performed an extensive search for weak periodic signals
in the frequency range 400 Hz to 2500 Hz using the burst records for 2203 GRBs
and 152 SGR flares. The study employs the Rayleigh power as a test statistic to
evaluate the evidence for periodic emissions. We find no evidence of periodic
emissions from these events at these frequencies. In all but a very few cases
the maximum power values obtained are consistent with what would be expected by
chance from a non-periodic signal. In those few instances where there is
marginal evidence for periodicity there are problems with the data that cast
doubt on the reality of the signal. For classical GRBs, the largest Rayleigh
power occurs in bursts whose TTE data appear to be corrupted. For SGRs, our
largest Rayleigh power, with a significance of 1%, occurs in one record for SGR
1900+14 (at 2497 Hz), and in no other outbursts associated with this source; we
thus consider it unlikely to represent detection of a real periodicity. From
simulations, we deduce that the Rayleigh test would have detected significant
oscillations with relative amplitude ~10% about half the time. Thus, we
conclude that high frequency oscillations, if present, must have small relative
amplitudes.
