So there was a 2 year gap in rifle date coded barrels and the normal consumer, or gunsmith would have to contact the factory for this information.
There are no publically accessible databases for Remington serial numbers.
With the hundreds of different Remington models produced over the past 200 years, it can sometimes be difficult to determine the age of your firearm.
REMINGTON MANUFACTURING DATE CODE stamped on LH top rear of barrel, 2 or 3 digit, (month first, year after) these will normally only be the last letters as seen below, The factory says all barrels are date code stamped, well I have found some that are not, or if they are, are so erratic stamping that trying to decipher them is impossible. Both were taken off Remington 760s, with the one on the left, a 30-06 that I bought new October 10, 1954. The one on the right again a 30-06, but with a shorter barrel that I made into a knock around quad rifle with pivot mounts.
(*) On 8/9/99, they stopped stamping the barrels with the date code.
Initially only offered with a 22 in barrel, in 1988 an 18 in version was introduced.