Tang and Ding [IEEE IT 67 (2021) 244-254] studied the class of BCH codes$\mathcal {C}_{(q,q+1,4,1)}$and their dual codes with$q=2^{m}$and established that the codewords of the minimum (or the second minimum) weight in these codes support 4-designs or 3-designs. Motivated by this, we further investigate the codewords of the next adjacent weight in such codes and discover more infinite classes of$t$-designs with$t=3,4$. In particular, we prove that codewords of weight 7 in$\mathcal {C}_{(q,q+1,4,1)}$support 4-designs for odd$m \geqslant 5$and they support 3-designs for even$m \geqslant 4$, which provide infinite classes of simple$t$-designs with new parameters. Another significant class of$t$-designs we produce in this paper has complementary designs with parameters 4-$(2^{2s+1}+ 1,5,5)$; these designs have the smallest index among all the known simple 4-$(q+1,5,\lambda)$designs derived from codes for prime powers$q$; and they are further proved to be isomorphic to the 4-designs admitting the projective general linear group PGL$(2,2^{2s+1})$as the automorphism group constructed by Alltop in 1969.

Formal method is a promising solution for precise software requirements modeling and V&V (Validation and Verification). However, domain experts are suffering from using complex mathematics formal notations to precisely describe their domain specific software requirements. Meanwhile, the lack of systematic engineering methodologies that can effectively encompass precise requirements modeling and rigorous requirements V&V makes the application of formal methods in industry still a big challenge. To tackle this challenge, in this paper, we present a domain experts centric approach to the formal requirements modeling and V&V in the domain of embedded control software. The major advancements of the approach are: 1) a domain-specific and systematic engineering approach to the formal requirements specification construction and 2) scenario-based requirements validation and verification requirements technique. Specifically, the approach offers a domain-specific template for formal specification construction through a three-step specification evolution process. For formal requirements V&V, diagrams are derived from formal specification and domain experts' concerned scenarios can be checked based on the diagrams. These modeling and V&V technologies are coherently incorporated in the approach and fully automated by a supporting tool. We have applied the approach real software projects of our industrial partners. The experimental results show that it significantly facilitates the formal modeling and V&V in industry.