Steiner systems S(2,4,2^m) for m ≡ 0 4 supported by a family of extended cyclic codes

04/04/2019

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by   Qi Wang, et al.

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In [C. Ding, An infinite family of Steiner systems S(2,4,2^m) from cyclic codes, J. Combin. Des. 26 (2018), no.3, 126--144], Ding constructed a family of Steiner systems S(2,4,2^m) for all m ≡ 2 4 from a family of extended cyclic codes. The objective of this paper is to present a family of Steiner systems S(2,4,2^m) for all m ≡ 0 4 supported by a family of extended cyclic codes. The main result of this paper complements the previous work of Ding, and the results in the two papers will show that there exists a binary extended cyclic code that can support a Steiner system S(2,4,2^m) for all even m ≥ 4. This paper also determines the parameters of other 2-designs supported by this family of extended cyclic codes.