Researches On Some Problems Of Linear Codes Over Two Classes Of Finite Rings

The paper investigates some problems of linear codes over the finite rings Z_2a + uZ_2a and the skew cyclic codes over ring GR?q,qm?+uGR?g,gm?.The details axe given as follows:?1?The first part,Mac Williams identity of linear codes and self-dual codes over Z_2a +uZ_2a are discussed.Mac Williams identity for the complete Gray weight enumerator is investigated firstly.Then,the gen-erator matrices of self-dual codes over Z2z +UZ_2a are given.Lastly,the torsion codes over Z_2a +uZ_2a are discussed and the generator matrices of torsion codes and the relationship between the torsion codes and the residue codes are also obtained.?2?The second part,the constacyclic codes over the principle ring Z2z + uZ_2a are studied.One hand,we firstly investigate the relation-ship between constacyclic codes over Z_2a + uZ_2a and constacyclic codes over Z_2a.The other hand,we obtain construction of self-dual codes by studying construction of ?—constacyclic codes over Z_2a+uZ_2a.?3?The third part,the skew cyclic codes over ring GR?q,qm?+uGR?q,qm?are studied.Firstly,we describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over GR?q,qm?+ uGR?q,qm?by a decomposition theorem.Furthermore,we give the generator polynomials of the duals of skew cyclic codes.