my professor told me that dimension of bch code is unknown in genelar, so i made a loop in SAGEMATH that create a BCH code of length $p^m-1$ over $GF(p)$ with every possible designed minimum distance $\delta$, and i asked for it dimension.

the output file ALWAYS ends with a $p^{m+1}$ code of dimension $1$ then there are no code of dimension less then $p+1$ so there are a "jump" of $p$. in fact the "jump" is ALWAYS a divisor of $m$ and there are a certain number of those. and things get nicer when $m$ is prime.

there is well behaved pattern here but i'm not too smart to tell a general formula. but i believe it can be done.

so my question is  : why the dimension of bch code still unknown  ?

My professor told me that dimension of bch code is unknown in general, so I made a loop in SAGEMATH that create a BCH code of length $p^m-1$ over $GF(p)$ with every possible designed minimum distance $\delta$, and I asked for it dimension.

The output file ALWAYS ends with a $p^{m+1}$ code of dimension $1$ then there are no code of dimension less then $p+1$ so there are a "jump" of $p$. in fact the "jump" is ALWAYS a divisor of $m$ and there are a certain number of those. and things get nicer when $m$ is prime.

There is well behaved pattern here but I'm not too smart to tell a general formula. But I believe it can be done.

So my question is: Why the dimension of bch code still unknown?