Step 1: Compare INDIA with its code JLGEF.
Line up the letters: I to J, N to L, D to G, I to E, A to F.
Step 2: Read off the shift pattern.
I to J is $+1$, N to L is $-2$, D to G is $+3$, I to E is $-4$, A to F is $+5$. The shifts follow $+1, -2, +3, -4, +5$.
Step 3: Apply the first two shifts to ROME.
R with $+1$ becomes S. O with $-2$ becomes M.
Step 4: Apply the next shift.
M with $+3$ becomes P.
Step 5: Apply the fourth shift.
E with $-4$ becomes A.
Step 6: Combine the coded letters.
Reading them together gives S, M, P, A, that is SMPA.
\[ \boxed{\text{SMPA}} \]