It is well known that maximum distance separable (in short, MDS) codes and linear complementary dual (in short, LCD) codes are very important in coding theory and practice. In 2023, Yue et al. [29] constructed three classes of LCD MDS codes via a class of TGRS codes with one twists, i.e., (∗)-TGRS codes. Recently, Wu et al. [31] also constructed several classes of LCD MDS codes via a class of TGRS codes with two twists. In this paper, we unify their constructions by defining the (∗)-(L,P)- twisted generalized Reed-Solomon (in short, (∗)-(L,P)-TGRS) code, give the parity-check matrix of (∗)-(L,P)-TGRS codes, and then construct four classes of LCD codes. Finally, some corresponding examples are given.

In this paper, we first study in detail the relationship between minimal linear codes and cutting blocking sets, recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking sets. As a direct result, minimal projective codes of dimension 3 and t-fold blocking sets with t ≥ 2 in projective planes are identical objects. Some bounds on the parameters of minimal codes are derived from this characterization. Using this new link between minimal codes and blocking sets, we also present new general primary and secondary constructions of minimal linear codes. As a result, infinite families of minimal linear codes not satisfying the Aschikhmin-Barg's condition are obtained. In addition to this, open problems on the parameters and the weight distributions of some generated linear codes are presented.