Low-income families in parts New Jersey will have the opportunity to move to better neighborhoods with better schools starting next year, after a federal judge this week directed the immediate implementation of an Obama-era desegregation rule.

Bergen, Passaic, Monmouth and Ocean counties are among 23 metro areas that will have to change how federal housing subsidies are calculated under a new formula designed to give poorer residents the chance to live in more expensive areas.

Advocates said the anti-segregation measure will break the cycle of relegating low-income families to poor neighborhoods.

"N.J. is a very diverse state and at the same time, one of the most segregated," said Nina Rainiero, a spokeswoman for the Housing and Community Development Network of New Jersey. "The ruling provides an opportunity for New Jerseyans who are struggling to make ends meet but want to raise their family in a safe, decent home in a great neighborhood with great schools."

Republican presidential candidate Ben Carson speaks to the crowd at an economic forum, Saturday, Jan. 9, 2016, in Columbia, S.C.

The U.S. Department of Housing and Urban Development and HUD Secretary Ben Carson were sued by a group of civil rights activists in October after the agency delayed implementing a rule that changed how Section 8 vouchers were calculated, court records show.

The rule directed housing voucher values be calculated using median rent values in each Zip Code, not in entire metropolitan areas. Because rental prices vary dramatically, using metro-wide numbers lowers the amount of a Section 8 subsidy -- largely disqualifying families from moving to higher-opportunity neighborhoods.

In her ruling, Chief Judge Beryl Howell said HUD's two-year delay to enact "small area fair market rents" in 2020 instead of 2018 was "arbitrary and capricious." She ordered the rules be implemented on Jan. 1.

HUD did not immediately respond to a request for comment Friday. In deciding to delay the rule implementation, the agency said it wanted to conduct further research to assess the impact of the changes, according to its blog post.

Those who qualify for Section 8 vouchers typically pay 30 percent of their income toward rent, the rest is paid by local housing authorities directly to landlords.

Using more targeted rental calculations broadens housing choices for families so that those who want to live in more affluent communities can receive higher subsidies to afford to do so, advocates argue.

For many low-income families, the opportunity to live in more expensive areas also means access to better-quality schools and lower crime rates.

"Federal housing policies are a major cause of the racial segregation that stubbornly persists to this day," said Sherrilyn Ifill, President and Director-Counsel of the NAACP Legal Defense and Educational Fund in a statement. "It's long overdue that our federal government remedy the massive disparities in wealth and education its policies continue to produce, and modest rules like this one play an integral role in leveling the playing field for Blacks, Latinos, and low-income Americans."

Karen Yi may be reached at kyi@njadvancemedia.com. Follow her on Twitter at @karen_yi or on Facebook.