古記 is read as こき (koki) and means ancient records.
こき
koki
こじき
Kojiki (earliest historical record of Japan, compiled in 712 CE)
こふどき
ancient fudoki compiled by imperial order in 713 CE
こくんこじき
Kojiki with Ancient Readings (by Nagase Masachi, 1803)
こじきでん
Commentary on the Kojiki (by Motoori Norinaga, 1798)
こきろく
historical document written without a particular addressee (e.g. a diary)
こまい
old rice
こと
ancient city
こさん
seniority
こしき
old style
ころう
old person (knowledgeable about events of the distant past)
ふるほんいち
secondhand book fair
こだいまい
ancient rice varieties