Research On The Depth And Period Distribution Of Linear Codes Over Several Classes Of Finite Rings

In this paper,the depth and period distribution of cyclic and constacyclic codes over some classes finite rings are studied.The details are given as follows:（1）The depth distribution and spectrum of cyclic and（1+u）-constcyclic codes over F₂+uF₂+vF₂+uvF₂ are studied.Firstly,the recursive algorithm for computing the depth of a codeword over the ring is given.Futhermore,by using the generarator polynomials of cyclic codes and（1+u）-constacyclic codes over the ring,the depth distribution and spectrum of cyclic codes of odd length and（1+u）-constacyclic codes of any length are obtained.（2）The depth spectrum of cyclic and constacyclic codes over F_p+uF_p,where u² =0,is studied.Based on the classification of kp,the depth spectrum of（1+lu）-constacyclic codes over the ring is completely determined by using their residue and torsion codes.（3）The period distribution of constacyclic codes over F_p+vF_p,where v²=v,is studied.The period of（l+vu）-constacyclic codes is transformed into the product of period of two corresponding constacyclic codes,by decomposing structure of such constacyclic codes over the ring.（4）The basic properties of skew negative-quasi twisted codes over Z₄+vZ₄ with v²=1 and their Gray images are studied.