The transactions on the new chain must not be valid on the old chain, and vice versa. So the old coins present in the new chain can only be spent as LNC. The two chains should then be independent after the split (or am I wrong here?)
I think merged mining should not be possible, because it would be a strength to maintain a relation by mining cost and value of coin. As suggested in Etlase's signature. I think merged mining would disturb that relation.
Have you already started work on this? Or is this your pre-project brainstorming?
WARNING: I am not an expert on this but I have a software engineering background and reasonable familiarity with the block chain and transaction graph data structures.
There are two ways to approach the problem.
1. Create a new LinearCoin P2P network entirely disconnected from the existing BitCoin P2P nodes.
This would require copying the entire BitCoin block chain to your new nodes before they could start relaying
transactions independent of the BitCoin P2P network. Theoretically, this keeps LinearCoin transactions from
spending BitCoins. HOWEVER, new LinearCoin transactions accessing these pre-fork blocks would be bitwise
copies of transactions that COULD spend on the BitCoin Chain. All it would take is for ANYONE to copy it and
submit it to the BitCoin network. You have to presume some malicious node WOULD.
Merged mining is theoretically possible in this case. Search for NameCoin they invented the concept.
Merged mining does NOT imply that LinearCoin block creation would be synchronized with BitCoin nor
that its difficulty be the same. It doesn't come for free though. You have to convince existing BitCoin
miners to support your chain as well. If they saw LinearCoins as valuable, supporting merged mining
would be as easy for them as supporting NameCoin.
2. Attempt to "peacefully" use the existing BitCoin P2P nodes for relaying transactions.
In this case your fork might be able to coexist on nodes along side the bitcoin fork. I think nodes do this by
default. However, long term support would require BUY-IN from the existing BitCoin developers because at
some point they will lock-in a block CHECKPOINT outside your fork. At that point BitCoin nodes would likely
stop relaying your transactions.
Mixed mining is this case should be even easier. However, again, it requires BUY-IN from the BitCoin developers.