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Since the publication of the first edition of this monograph, the following advances on constructing combinatorial t-designs with linear codes have been made: _ A generalization of the Assmus-Mattson theorem for linear codes over finite fields [Tang, Ding and Xiong (2019)]. _ The discovery of an infinite family of near MDS codes over finite fields supporting an infinite family of 2-designs [Ding and Tang (2020)]. _ The discovery of an infinite family of BCH codes over GF(22m+1) of length 22m+1 +1 supporting an infinite family of 4-designs [Tang and Ding (2021)]. These advances are the main motivation for the second edition of this monograph. The Assmus-Mattson theorem was developed in 1969, and has been used to construct many infinite families of 2-designs and 3-designs in the past 50 years. However, some infinite families of linear codes do support t-designs, but the tdesign property of the incidence structures defined by the linear codes cannot be proved with the Assmus-Mattson theorem and the automorphism group of the codes. In the past 50 years, a strengthening of the Assmus-Mattson theorem for special binary linear codes was documented in Calderbank, Delsarte and Sloane (1991) and several analogues of the Assmus-Mattson theorem in other contexts (for example, certain association schemes [Morales and Tanaka (2018)], codes over Z4 [Tanabe (2000)], and rank-metric codes [Byrne and Ravagnani (2019)]) were developed. The Assmus-Mattson theorem for matroids developed in Britz, Royle and Shiromoto (2009) does contain the original Assmus-Mattson theorem as a special case, but it becomes the Assmus-Mattson theorem when it is applied to codes. The generalized Assmus-Mattson theorem for linear codes over finite fields developed in Tang, Ding and Xiong (2019) turns out to be useful, and will be the topic of a new chapter in this second edition.