The Depth Distribution Of Linear Codes On Finite Field

The depth spectrum and depth distribution are two important parameters in linear codes structure studying. The research of depth character on linear codes help us have a good knowledge about linear codes structure and make us can have a good use of error-correcting codes. On the other hand, we can classify linear codes according to depth equivalence.This paper focuses mainly on the relationship of depth distribution and period distribution of linear codes. On finite field, we find a way to get the period distribution according to the depth distribution of lindar codes. Then, we get a conclusion about the relationship of depth distribution and the period of infinite sequences. The depth character of linear codes over ring F₂ + uF₂ also has been studied in this paper. Then we give the depthspectrum and depth distribution of linear codes (especially the cyclic codes). At the same time, we find a way to get generators of cyclic codes over ring F₂ + uF₂ without decomposingpolynomial xⁿ-1.