Two more men — including a former regional director of the Department of Homeland Security’s Federal Protective Service — have been sentenced in connection with a far-reaching scheme to win lucrative government contracting work meant for small, minority-owned businesses, authorities said.

Derek Matthews, 47, who once served as regional director of the Federal Protective Service, was sentenced Thursday to a year and three months in prison, and David Sanborn, 60, a government-contracting executive, was sentenced Friday to two years in prison, authorities said. Federal prosecutors said the men were part of a ring that defrauded the government for more than a decade, running a scheme that netted them more than $31 million in government contracts they did not deserve.

With many others, prosecutors said, the men set up a shell company and installed a figure­head minority owner so they could win government contracts designed for minority-owned businesses. Though the work their employees did was satisfactory, prosecutors said, it should have been done by legitimate minority-owned businesses.

Matthews, prosecutors said, accepted $12,500 in bribes from the group to help steer government contracts their way.