There are a bunch of different Linux kernel options for MIPS computers. This page has links to the various possibilities.

• Standard linux kernel. As of 2.6.18.2, this doesn't include any architecture support for Broadcom 4780 SOCs. It has MIPS support for other architectures though.
• Linux-MIPS kernel. The Linux-MIPS project has a GIT repository where they include a bunch of additional MIPS-related stuff into the vanilla Linus kernel. Still nothing for 32-bit Broadcom chips like BCM4780, which is too bad since they track the Linus kernel very closely.
• OpenWRT project. In their subversion repository, "kamikaze" branch, there are directories brcm-2.4 and brcm-2.6 under target/linux. This adds BCM4780 architecture support. Unfortunately it is a patch against 2.6.17 (currently), so clearly it is not updated as aggressively as the linux-mips kernel.
• The standard Asus firmware comes with Linux 2.4.20, probably with modifications. This source is part of the GPL firmware.