Yes—compact tripods in that size range do exist, but the options are limited and you may need to compromise on maximum height.

From the answers provided:

• The Velbon V-Pod is listed as folding to about 29cm and extending to about 101cm, so it matches your folded-size target and just meets your minimum height requirement.
• The Velbon CX Mini folds to about 30cm, but only reaches 64cm, so it would not count as full-size by your definition.
• One answer notes that Manfrotto models did not appear to go below about 42cm folded, so they may not suit your bag-size requirement.
• Three Legged Thing was also suggested as a brand worth checking, as they offer compact tripod designs.

In general, the shorter a tripod folds, the more likely it is to rely on more leg sections or a reversible/folding design, which can trade off some rigidity or speed of setup. If your priority is fitting inside a bag, the Velbon V-Pod sounds like the clearest match from the answers given.