Research On Several Classes Of Constacyclic Codes Over Finite Rings

With a more deeply study in error-correcting codes over finite chain rings, constacyclic codes over several finite rings which are not finite chain rings also have been considered by some authors. In this paper, we mainly study the structures of some classes of constacyclic codes over finite rings and also the properties of their images under the Gray maps. The details are given as follows:(1)We introduce the structure of (1+uk)-constacyclic codes of odd length n over the ring F2+uF2+…+ukF2and necessary condition for the existence of self-dual codes, and also give the properties that the Gray image of (1+uk)-constacyclic codes and their dual codes are orthogonal.(2)(1+λu)-constacyclic codes over F2m+uF2m are studied, we give the structure of (1+λu)-constacyclic codes. Some Gray maps from one ring to another are defined, and we get some properties of the Gray image.(3)We study (1+λv)-constacyclic codes of arbitrary length over Fpm+vFpm, and obtain their generator polynomials, also the specific (1-2v)-constacyclic codes of length ps are obtained. Finally, we introduce a Gray map from Fpm+vFpm to Fp2m and show that the Gray image of (1-2v)-constacyclic codes of length n over the ring are quasi-cyclic codes of length2mn and index m over Fp.