The passwords in Mega Man 3 have a rather easy structure: one red dot memorizes the numbers of E-cans, the other dots (both blue and red) memorize which stages have been cleared. In particular, each "stage-dot" memorizes two cleared stages.
The most advanced password leads the player directly to the entrance of the Skull Fortress, with 9 E-cans.
A complete Mega Man 3 password generator can be found following this link to the fan-site Mega Man Home Page.
In the Mega Man The Wily Wars remake, a save system replaced the passwords.