Some Researches On The Duals Of Classic Binary Irreducible Cyclic Codes And Quantum Error-Correcting Codes

In this article we intend to discuss binary irreducible cyclic codes and quantum error-correcting codes.Chapter 1 is an account of the prerequisite mathematics on the two type of codes.Chapter 2 provides new constructions on the duals of binary irreducible cyclic codes. We generalized results of [13].The main aim is to discuss weights of in chapter 3. We get better results than Corollary9 in [13].We centrate on the open problems in [13] in chapter 4. There are only finite solutions satisfy the eqution m = 2^th + 2^h - 1. This fact promises we guess the density of solutions.The last chapter is on quantum codes. K. Feng and C. Xing[27] recently had given a new construction. In virtue of their results, we defined representive number and established several new quantum error-correcting codes.