Rereading the SAE rules, I find the wording for the Fire Linked trait a little confusing. 

Suppose I have a weapon with ROF:1, ACC 4+, Imp 1, and Dam 4 with Fire Linked
Suppose I have four of them firing at one target.

If I am reading right, I would roll only 1 die, and if it hit I would cause 4 hits, for a total of 16 damage (assuming I got past the enemys shields). 

If I had six weapons, 1 die could cause 6 hits, for potentially 24 damage.

Am I correct in my interpretation?