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Combinatorial t-designs have been an important research subject for many years, as they have wide applications in coding theory, cryptography, communications and statistics. The interplay between coding theory and tdesigns has been attracted a lot of attention for both directions. It is well known that a linear code over any finite field can be derived from the incidence matrix of a t-design, meanwhile, that the supports of all codewords with a fixed weight in a code also may hold a t-design.doi:10.3934/amc.2020088 fatcat:uqgxecvpvzaudfquh3fesy6oa4