An infinite family of antiprimitive cyclic codes supporting Steiner systems $$S(3,8, 7^m+1)$$

Coding theory and combinatorial t-designs have close connections interesting interplay. One of the major approaches to construction is employment error-correcting codes. As we all known, some been constructed with this approach by using certain linear codes in recent years. However, only a small number infinite families cyclic holding an family 3-designs are reported literature. The objective paper study antiprimitive determine their parameters. By parameters these dual, presented also explicitly determined. In particular, complements supports minimum weight codewords studied code form Steiner system. Furthermore, show that admit 3-transitive automorphism groups.