Media General Corp., Richmond-based communications and newsprint firm, reported record 1981 earnings and revenues.

Net income rose to $31.6 million ($4.41 a share) from $28.3 million ($3.91) as revenues climbed to $366.5 million from $332.5 million in 1980.

Media General's operations include the Richmond Times-Dispatch, financial journals, broadcasting properties and a newsprint subsidiary.

The Tultex Corp., a Martinsville, Va., holding company with textile and apparel operations in Virginia and North Carolina, also reported record sales and profits for its fiscal year ended in November.

It reported profits rose to $10 million from $7.5 million the previous fiscal year, while sales increased 5.6 percent to $192 million.

Order backlogs declined, but William J. Frank, Tultex president, said he was optimistic they would increase as the economy recovers later this year.

F & M National Corp., a banking firm in Winchester, Va., reported 1981 earnings slipped to $2.17 million ($1.30 a share) from $2.18 million ($1.29). In the fourth quarter, earnings fell to $534,000 (33 cents) from $749,500 (44 cents) a year earlier.

Year-end assets, however, increased by $11.7 million to $221.3 million.