ity - check ▁matrix ▁for ▁the ▁original ▁code ▁and ▁vice ▁vers a . ▁ ▁The ▁dual ▁of ▁the ▁dual ▁code ▁is ▁always ▁the ▁original ▁code . ▁ ▁Self - du al ▁codes ▁A ▁self - du al ▁code ▁is ▁one ▁which ▁is ▁its ▁own ▁dual . ▁This ▁implies ▁that ▁n ▁is ▁even ▁and ▁dim ▁C ▁= ▁n / 2 . ▁If ▁a ▁self - du al ▁code ▁is ▁such ▁that ▁each ▁code word ' s ▁weight ▁is ▁a ▁multiple ▁of ▁some ▁constant ▁, ▁then ▁it ▁is ▁of ▁one ▁of ▁the ▁following ▁four ▁types : ▁Type ▁I ▁codes ▁are ▁binary ▁self - du al ▁codes ▁which ▁are ▁not ▁doub ly ▁even . ▁Type ▁I ▁codes ▁are ▁always ▁even ▁( every ▁code word ▁has ▁even ▁Ham ming ▁weight ). ▁Type ▁II ▁codes ▁are ▁binary ▁self - du al ▁codes ▁which ▁are ▁doub ly ▁even . ▁Type ▁III ▁codes ▁are ▁t ern ary ▁self - du al ▁codes . ▁Every ▁code word ▁in ▁a ▁Type ▁III ▁code ▁has ▁Ham ming ▁weight ▁divis ible ▁by ▁ 3 . ▁Type ▁IV ▁codes ▁are ▁self - du al ▁codes ▁over ▁F 4 . ▁These ▁are ▁again ▁even . ▁ ▁C odes ▁of ▁types ▁I , ▁II , ▁III , ▁or ▁IV ▁exist ▁only ▁if ▁the ▁length ▁n ▁is ▁a ▁multiple ▁of ▁ 2 , ▁ 8 , ▁ 4 , ▁or ▁ 2 ▁respectively . ▁ ▁If ▁a ▁self - du al ▁code ▁has ▁a ▁generator ▁matrix ▁of ▁the ▁form ▁, ▁then ▁the ▁dual ▁code ▁ ▁has ▁generator ▁matrix