On The Structure And Some Properties Of Quasicyclic Codes

In this thesis, we first introduce the basic knowledge and some results of error-correcting codes and cyclic codes. We discuss the structure of quasicyclic codes, regarding them as F_q[x]/ < x~m -1 > -submodules of F_q~l [x]/ < x~m - 1 >. Next we give the detailed proof of two results in reference [2], and calculate four quasicyclic codes. After that we discuss some properties of quasicyclic codes, including the relation between 1-generator quasicyclic codes and multi-generator quasicyclic codes, i.e., several multi-generator quasi-cyclic codes are equivalent to certain 1-generator quasicyclic codes under some conditions. We calculate the dimension of 2-generators quasicyclic codes afterwards. After that we estimate the minimum distance of quasicyclic codes. Finally, we give some examples of two quasicyclic codes of 2-generators.