President Carter yesterday proposed a standby gasoline rationing plan that links the right to buy gasoline to automobile, truck and bus registrations.

Carter also said he will ask Congress to approve less stringent standby authority for limiting gas sales during all or part of the period each week from Friday noon until Sunday midnight, for restricting summer cooling and winter heating in most nonresidential buildings, and for restricting lighted advertising signs and window displays.

The gasoline rationing plan would be used only in the event of a "severe energy supply interruption," which was not defined in the proposal. The plan includes no specific amounts of gasoline that would be available for each vehicle, since that would depend on the degree of any oil shortage.

The rationing plan would work this way:

Owners of registered motor vehicles would get in the mail every three months a gasoline ration check which could be redeemed at a local bank or other designated institution for ration coupons.

The ration check would be for a certain number of gallons for that three months. The amount would vary for each class of vehicle, with trucks and buses getting larger allotments than passenger cars, and motorcycles getting still smaller amounts. All passenger cars would get the same allotment.

The ration coupons would be required to buy gasoline. The coupons could be bought and sold legally in a so-called white market. Anyone who did not need all of his coupons could sell them. The government would not supervise such sales.

Essential public services would get "priority allotments" -- basically, however much fuel is needed by police, firefighters, ambulance drivers and so forth.

Farmers would get additional allotments for tractors and other gasolinepowered equipment.

Last year the average passenger car used 693 gallons of gas, according to the Department of Energy, an average of about 58 gallons a month.

If the president decided that a shortage required rationing and chose to reduce gasoline consumption by, say, 20 percent, that would mean a monthly allowance of about 45 gallons per car.

Each state would get a percentage of the ration coupons to distribute as the state sees fit, "to deal with hardship cases." Out of that allotment, states would be required to meet any special needs of handicapped people.

Congress has 60 days in which to approve the proposal. DOE estimates that it needs $53.4 million this year and next to set up the rationing plan, a process that would take six to eight months.

It would take $350 million more to start rationing, DOE said, and could take up to 90 days. After that, the program would cost $400 million each three months.

The ration coupons printed during the 1973-74 Arab oil embargo would be numbered and used in the first three months of rationing.

An analysis of the impact of rationing, DOE said, showed that income would be transferred "among geographic regions and among income classes, as individuals and businesses with more coupons than they need sell ration rights to others who are willing to pay for these extra rights.

"Lower-income households would tend to be net sellers of ration rights, and would therefore receive net additional income under the rationing program," the analysis concluded. Regions such as much of the West would be a net loser under the program, since average driving distances there are greater.

Diesel fuel is not affected by this plan, but DOE said it is addressing it separately.

The plan differs from the one sent to Congress in January 1977 by President Ford primarily in basing allotments on registered vehicles instead of drivers' licenses, and in using ration checks instead of forms drivers would have had to fill out at the beginning of the program.

These changes make the plan "more quickly implementable and more effective," DOE said.