Research On Linear Codes Over One Finite N On-chain Ring

Coding over rings have been studied extensively in the past decade.Re-cently,several finite non-chain rings,new families of rings have been intoduced in coding theory,aruong which R = Fl[u,v]/<uk,v2,uv-vu>is concerned in this paper.The details are given as follows:1?The Mac Williams identities with respect to RT metric for linear codes over R1=Mn×s(F2[u,v]/<uk,v2,uv-vu>)are studied.The definitions of the Lee complete p weight enumerator and the exact complete p weight enumerator over R1 are defined,and the MacWilliams identities with respect to RT metric for these two weight enumerators of linear codes over R1 are obtained.Finally,we give two examples to illustrate the results are obtained.2?We investigate the support weight distribution of codes over R3=Fp + uFp + vFp + uvFp,where u2 = u,v2 = v and uv = vu.We get the main results about a Macwilliams-type identity on the support weight enumerator of codes over R3.Finally,we give two examples to illustrate the identity.3?The relationship between cyclic codes and quasi-cyclic codes is studied.Firstly,codewords of quasi-cyclic codes are divided into l parts.The length of each part is m,each part can be viewed as a cyclic block.According to the definitions of module and cyclic codes,we can get a special of quasi-cyclic codes.Finally,we give some numerics.