|Spoiler Alert: This page contains spoilers. Read at your own risk.|
Cardinal Codes is the name given to the 16 fundamental Magic Sequences that are postulated by the 'Cardinal Code Hypothesis'. This theory states that there are 16 fundamental Magic Sequences, from the Four Great Systems and Eight Major Types with the corresponding positive and negative poles. The theory states that any magic from the Four Great Systems can be recreated by using various combinations. 
Within Modern Magic, effects occur after redefining an object after phenomenon rewriting. The driving force behind the change is defined in the Magic Sequences; however, the driving force would not exist without defining what happens after the magic affects the target.
The Cardinal Codes on the other hand are able to create the driving force themselves. They are Magic Sequences that literally define 'Speed', 'Weight', 'Movement', 'Oscillation', 'Convergence', 'Dispersal', 'Absorption', and 'Release'; the Eight Major Types. Rather than having an overall effect on the Eidos, these act on a single object and render them possible. Magic created by using the Cardinal Codes doesn't need to define the phenomena it alters, instead it recreates the driving force itself.
However, the theory is incorrect according to Shiba Tatsuya. There are spells within the Four Great Systems that cannot be recreated using the Cardinal Codes. They do exist as building blocks, but not every magic can be recreated.
It is revealed that Ichijou Masaki also doubts the validity of the Cardinal Code Hypothesis. His doubt is based on a gut feeling, and the belief that the systems used to classify the magic, work conveniently. 
Discovered Cardinal Codes
Weight-Type Magic - Developed by Kichijouji Shinkurou of Third High School. The first and only Cardinal Code discovered on record. His magic, 'Invisible Bullet' uses the Cardinal Code he discovered. 'Invisible Bullet' cannot be defended against with 'Data Fortification', or any other ability that defends against rewriting the Eidos of the target. Also, there is less to define, making the Magic Sequence smaller and thus faster and more efficient than other magics.
Kichijouji Shinkurou - Is able use the Cardinal Code for Weight-Type Magic that he discovered.