It depends on which retirement system you worked. If you paid Social Security tax on your earnings, you are covered.
Up until 1984, workers for the federal government were covered under the Civil Service Retirement System (CSRS). If you worked for a federal agency during these years, you did not pay Social Security tax on your earnings and you were not covered by Social Security.
But in 1984, a second retirement system, the Federal Employees Retirement System (FERS), was introduced. Federal workers hired under FERS are covered by Social Security because they pay Social Security taxes. Also, some workers covered by CSRS chose to switch to FERS. They, too, pay Social Security taxes and are therefore covered providing that they have 40 credits.
Both workers under FERS and CSRS workers are covered under the Medicare program because they pay Medicare taxes on their federal earnings.
More Information
Windfall Elimination Provision
How the Windfall Elimination Provision Can Affect Your Social Security Benefits
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