There is a well known brand, sold by a number of DIY chains, that has a similar issue. They use off the shelf chips with a finite number of codes and have no jamming or brute force detection at all. Wall down most streets and look for the bright yellow solar powered box.
Wired systems have come a long way. Even basic systems now use either digital monitoring of sensors or a wiring scheme called eol that has two or more resistors. Open circuit the wire, thats a tamper. Short it, that's a tamper too. You need to know the exact two resistors and what contacts they are sat on and even a few mS anomaly on the wiring will wake more sophisticated systems and start all sorts of monitoring.
AFAIK wireless is only considered secure for insurance with encryption on all end points and anti jamming.
Basic code hopping would defeat this issue as the co shouldnt speak to any device it has no knowledge of. OK not perfect but better than nothing at all.
Biting the hand that feeds IT
