What are known ways to construct linear cyclic codes with minimum distance at least a given number $d$ (and a reasonable rate)?
I could only find two known methods: BCH codes and Quadratic residue codes.
Are there other methods described in books, or papers (or that you're willing to describe here)?
Clarification: I'm interested to know different approaches to constructing cyclic codes in a way that allows us to say something about the distance. It seems like usually it's rather hard to say something about the distance, so I'm interested in collecting examples when we are able to say something about it.