Designs from the Narrow-Sense Primitive BCH Codes c_((q,q~m-1,δ_3,1))

摘要

The interplay between coding theory and t-designs has been a very interesting topic for researchers. It is well known that the supports of all codewords with a fixed weight in a code may form a t-design under certain conditions. In this paper, we will determine explicitly the parameters of many infinite families of 2-designs from the extended of the primitive BCH codes c_((q,q~m-1,δ_3,1)) with δ_3 = ((q-1)q~(m-1))-1-q~(「(m+1)/2」) and odd prime q given by Li et al. [18] and point out that their duals hold 2-designs.