Correct, but since you’re asking about Cody it’s worth noting under which conditions you can link into a move that you couldn’t under normal conditions.
One condition is when you score a counter hit (CH). This gives you more you frame advantage, and allows you to perform combos like CH close st.HP, cr.hp.
Another way to perform a link like that is to ensure that the close st.hp hits sufficiently meaty. Close st.HP has 4 active frames. If it connects on the first active frame, the frame advantage is +6f. If it connects later than that, you theoretically get more frame advantage (eg. 2nd active frame = +7f, 3rd active frame = +8f, last active frame = +9f). I said “theoretically” because not all active frames of a move result in the same hit-stun. Hitting on the first active frame might give more hit-stun than hitting on the subsequent ones, so the effective frame advantage might not be the same. I’m not sure about Cody’s close st.hp though, so maybe someone else can shed some light (or preferably just test it yourself in training mode). Meaty attacks can also get the benefit of landing as counter-hits, which yield even more frame advantage.
The last way (that I know of) to link into moves that you can’t under normal conditions is to perform a trade option select, where your move gets interrupted by another that causes less hit stun than the recovery + remaining active frames. Eg. Cody’s close st.HP essentially has 13f + 3f effective recovery frames if it hits on the first active frame. If he trades with a crouch tech attempt (which typically causes 13f of hitstun), his recovery is essentially cut by 3f. If you buffer another move during the recovery of st.hp, it will come out after the trade and it will combo provided it’s quick enough.
Forgot that some normals can also be FADC’d to provide linking opportunities, eg. Ryu’s close st.mp FADC into st.mp. Even though the link should work without FADC according to the frame data, reel caused by the first attack pushes the opponent out of range. FADCing it allows you to link another attack. Impractical though.