MDS constacyclic codes over finite fields are important in both theory and practice. In this paper, all [q + 1,2,q] and [q + 1,3,q − 1] MDS λ-constacyclic codes over GF(q) are characterized, three classes of [q + 1,4,q − 2] MDS λ-constacyclic codes over GF(q) are constructed, and four classes of [q + 1,k,q − k + 2] MDS λ-constacyclic codes over GF(q) for variable k are presented. Rationales for distinguishing the class of cyclic codes, the class of λ-constacyclic codes with λ≠ 1, and the class of non-constacyclic linear codes are given...
