I have the following simplified and shortened tables:

table_a:
 label  type  code
 -----  ----  ----
'----' 'ab'  '0123' <-- label will     be changed
'----' 'ab'  '8234' <-- label will     be changed
'----' 'ab'  '9176' <-- label will not be changed
'----' 'cd'  '4554' <-- label will     be changed
'----' 'cd'  '5122' <-- label will     be changed
'----' 'cd'  '7777' <-- label will not be changed

table_b:
 label  type  code
 -----  ----  ----
'KOTA'  'ab' '01'  <-- will     match
'KOTA'  'ab' '8'   <-- will     match
'KOTA'  'ab' '923' <-- will not match
'RRHW'  'cd' '4'   <-- will     match
'WWUP'  'cd' '512' <-- will     match

I update table a with this query:

UPDATE table_a AS a
  RIGHT JOIN table_b AS b
     ON a.type = b.type
    AND LEFT(a.code, LENGTH(b.code)) = b.code
    SET a.label = b.label;

It works but in the actual case in our database this is very slow. There’s no way I can change the database (adding an index or . . ). Is there a better (faster) way to update table a?