The case is People v. James, just decided today. Here's the core of the analysis:
[As Heller holds, “the right secured by the Second Amendment is not ... a right to keep and carry any weapon whatsoever in any manner whatsoever and for whatever purpose.” Rather, it is the right to possess and carry weapons typically possessed by law-abiding citizens for lawful purposes such as self-defense. It protects the right to possess a handgun in one’s home because handguns are a “class of ‘arms’ that is overwhelmingly chosen by American society” for the lawful purpose of self-defense.
As the court’s discussion makes clear, the Second Amendment right does not protect possession of a military M-16 rifle. Likewise, it does not protect the right to possess assault weapons or .50 caliber BMG rifles. As we have already indicated, in enacting the Assault Weapons Control Act of 1989 and the .50 Caliber BMG Regulation Act of 2004, the Legislature was specifically concerned with the unusual and dangerous nature of these weapons. An assault weapon “has such a high rate of fire and capacity for firepower that its function as a legitimate sports or recreational firearm is substantially outweighed by the danger that it can be used to kill and injure human beings.” (§ 12275.5, subd. (a).) The .50 caliber BMG rifle has the capacity to destroy or seriously damage “vital public and private buildings, civilian, police and military vehicles, power generation and transmission facilities, petrochemical production and storage facilities, and transportation infrastructure.” (§ 12275.5, subd. (b).) These are not the types of weapons that are typically possessed by law-abiding citizens for lawful purposes such as sport hunting or self-defense; rather, these are weapons of war.
I can't speak to the wisdom of a .50-caliber ban, but this seems to be a sensible interpretation of Heller's test for what "arms" are protected. Moreover, as I argue in my forthcoming Implementing the Right to Keep and Bear Arms in Self-Defense article, this is also consistent with a sensible interpretation of the right to keep and bear arms in self-defense. In my article, I argue that Heller's "typically possessed by law-abiding citizens for lawful purposes" test is flawed. But, among other things, I argue that the right to bear arms for self-defense shouldn't be seen as infringed by restrictions that don't materially interfere with the right to self-defense; and a ban on .50-caliber rifles doesn't materially interfere with self-defense (see PDF pages 12-19 and 48, as well as PDF pages 37-42 for the discussion of interpreting the scope of "arms" post-Heller).
This doesn't speak, of course, to the right to keep and bear arms for other reasons, such as deterrence of government tyranny and the like. But I leave that questions to others (much as the Court did in Heller); writing 100+ pages on the right to bear arms in self-defense is enough for me.