Boxers are notorious for farting, and all 3 of mine do (2 more so than the 3rd). Considering that boxers and bulldogs are related, you may be in for the long haul. Changing the food may help, but in doing so you'll probably have a better chance at reducing the stinkyness than completely eliminating them. You never know though, so give it shot. I'd try a premium kibble such as Innova EVO, Orijen, Canidae etc., over any mass-marketed brand in supermarkets which are usually loaded with grains and other unnecessary ingredients that can contribute to more waste and more gas.
http://www.dogfoodanalysis.com/dog_food_reviews/
http://www.healthyhappydogs.com/APIarticle