Construction Of Quasi-Twisted Codes Over Finite Rings

As the generalization of the constacyclic codes and quasi-cyclic(QC)codes,quasi-twisted(QT)codes are an important class of linear codes.In this paper,we mainly study the quasi-twisted codes over finite rings.We research the 1-generator quasi-twisted codes over integer residue class ring Zq,finite chain ring F2 + uF2 and matrix ring M2(F5),respectively.Firstly,we mainly research 1-generator QT codes over Zq.Give the generator polynomials and the weight distribution of the constructed 1-generator QT codes over Z25.Secondly,we discuss the minimal generating sets of the three types of 1-generator(1 + u)-quasi-twisted codes over the finite chain ring F2 + uF2.With the help of Gray map,we obtain some good codes over finite field F2.Finally,we study the cyclic codes over the ring M2(F5).Give the method of the decomposition of xn-1 and construction of cyclic codes over M2(F5).The mainly basis of these works is the isomorphic between the ring M2(F5)[x]and F25[Y,9]/(Y2-1)[x].