You are fortunate to own the Linn CD12.
Yeah real funny story, it's the very last MkIII model with 4 x "K" versions of the PCM1704 and PMD200 hdcd.
Got it in to look at from a friend who's not short of a buck, it had intermittent 5 seconds digital noise every hour or so digital in the right channel very hard to trace, everything was smd and multilayer pcb, spent a 1/2 a day on it, impossible to fix down to component level, and with no circuit diagram, Linn won't give/sell them to anyone even to distributors, needed a new main board they kept saying you'll have to send it back.
Linn wanted $5Kaud for a new one, and they wouldn't sell me one. They said, I had to post the whole (12kg) unit back, but not back to them, but to Aus Linn distributor first, then they would send it back to them in the UK, I would have pay for post every which way, and another $1k for Linns labour plus the $5k for the board. I told the very well off owner, he knew a ripoff straightaway, and he said f*** that, give me $100 and keep it for the aluminium case. So I got it for $100 and my 1/2 day of labour and dealing with Linn.
Up shot, I worked on this thing for at least 8 days on and off, for the next 6mts in my spare time. Dismantling re-soldering in sections every smd joint, re-assembling and trying it out in between sections, almost gave up and was going to advertise it as intermittent faulty, and then one day turned it on and bingo no noise, it's been noise free now for 2 years and sounds magnificent, and to this day I have no idea how I fixed it.