Thanks for the link to that study. Looks like some good reading material there. I searched it for scalation information and saw that Table 2 (page 24) seem to match up with the study I mentioned.
I have done multiple spawns with two leather males and a female that had a partial linear row on each side.
https://www.koiphen.com/forums/showt...u-Kujaku-spawn . I got substantial numbers of all scale types as shown in the bottom row of combination #9 in that table. We know the males had to be ssNn. So the female must be SsNn linear even though the row of lateral scales is not complete. I think she could have been SSNn just based on appearance, but she would have only produced fully scaled and linear fry.
You mentioned that yours have "sporadic scales on their sides". One key is whether those scales are all along the lateral line (probably still linear genetics), or if they look random, some high, some low (scattered scale genetics). Probably linear, since most breeders don't raise the scattered scaled fry.
Kirpichnikov, who is referenced, is the author of the study that I mentioned, which is at
https://www.fao.org/4/b3310e/b3310e14.htm
I was thinking it was written in the 1960's because none of the references at the end were newer than 1968. But it may have been written later since the link in your note mentioned papers by that author from 1981 and 1999.