Encryption

The positions of the letters $A,B,D,H,P,Y$ in the alphabetic system are $1,2,4,8,16,25$ , respectively.

First code : $AD\leftrightarrow \overline {pos_Apos_D}-\sqrt {pos_A\times pos_D}\equiv 14-2=12$

Second code : $BH\leftrightarrow \overline {pos_Bpos_H}-\sqrt {pos_B\times pos_H}\equiv 28-4=24$

Third code : $AP\leftrightarrow \overline {pos_Apos_P}-\sqrt {pos_A\times pos_P}\equiv 116-4=112$

So, $PY\leftrightarrow \overline {pos_Ppos_Y}-\sqrt {pos_P\times pos_Y}=1625-20=\boxed {1605}$ .

The first letter is the same as in the order of alphabets, the second letter is the square root of that:

$AD=(A=1)(\sqrt{D}=\sqrt{4}=2)=12$

$BH=(B=2)(\sqrt{H}=\sqrt{8}=2\sqrt{2})=22\sqrt{2}$ (I think something is wrong in the queston)

$AP=(A=1)(\sqrt{P}=\sqrt{16}=04)=104$

$PY=(P=16)(\sqrt{Y}=\sqrt{25}=05)=\boxed{1605}$