  The activity of the soft gamma ray repeater SGR 1806-20 is studied in
correlation with the EXPLORER and NAUTILUS data, during the year 2004, for
gravitational wave (GW) short signal search. Corresponding to the most
significant triggers, the bright outburst on October 5th and the giant flare
(GF) on December 27th, the associated GW signature is searched. Two methods are
employed for processing the data. With the average-modulus algorithm, the
presence of short pulses with energy Egw \geq 1.8 x 10^49 erg is excluded with
90% probability, under the hypothesis of isotropic emission. This value is
comparable to the upper limits obtained by LIGO regarding similar sources.
Using the cross-correlation method, we find a discrepancy from the
null-hypothesis of the order of 1%. This statistical excess is not sufficient
to claim a systematic association between the gravitational and the
electromagnetic radiations, because the estimated GW upper limits are yet
several orders of magnitude far away from the theoretically predicted levels,
at least three for the most powerful SGR flare.
