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Some Researches on the Duals of Classic Binary Irreducible Cyclic Codes and Quantum Error-Correcting Codes

Author: SunGuangRen
Tutor: XingChaoPing
School: University of Science and Technology of China
Course: Basic mathematics
Keywords: the duals of binary irreducible cyclic codes quantum error-correcting codes
CLC: O157.4
Type: PhD thesis
Year: 2006
Downloads: 106
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Abstract


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 = 2th + 2h - 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.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Coding theory ( on behalf of the digital theory )
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