It has been known for decades that the codewords of a fixed weight in a code may hold a t-design. However, only a small amount of progress on the construction of t-designs from codes has been made so far. It was also proven that the automorphism groups of the extended codes of the narrow-sense primitive BCH codes over finite fields are doubly transitive and these extended codes hold 2-designs. But little is known about the parameters of these 2-designs. The objective of this extended abstract is to present the parameters of some 2-designs held in these extended codes of some classes of narrow-sense primitive BCH codes.
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