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1. Galois, it is usually said, coined the word group at this time and introduced the concept of normal subgroup.

2. What had led Galois to invent this theory?

3. Have you ever heard Galois?

4. Based on Galois theory of definite field, using the square prime sequence, the code function of basic prime code is modified and extended.

5. And once Galois had started to work on it, had he made any false starts,(sentencedict.com/galois.html) gone down any dead ends?

6. An arithmetic unit, which can perform all dual Galois fields' arithmetic operations, including addition, subtraction, multiplication, squaring, inversion and division, is designed for the ECC.

7. An implementation for computing multiplicative inverses in Galois fields GF ( 2 m ) is presented.

8. The underlying algebraic structures are composite Galois fields GF (( 2~ n ) ~ m ) in a standard base representation.

9. All of the below statements on Galois connections can thus easily be converted into statements about antitone Galois connections.

10. Basing on the analysis of the multiplication in Galois, this paper designed a RS (10, 8) encoder which can correct one error and offers the process of FPGA implementation.

11. The group which is founded by Galois and Abel and the theory which is proposed by Klein provide the tool from the second stage to the third stage of the geometry.

12. This work organised the known theory of permutation groups and its relationship with Galois Theory.

13. A number of ancient problems concerning Compass and straightedge constructions were finally solved using Galois theory.

14. Following the same route to study the one-dimensional quasiperiodic sequences, we first establish two kinds of tight-binding models for Galois sequence: the on-site model and the transfer model.

15. The polarities check ability, minimum code distance and capacity of correct single bit error of CRC-CCITT are proved by using galois field polynomial theory.

16. On the dialectic point of view, the influences of Cauchy's systematical study on the theory of permutation to understanding Galois Theory to mathematicians in France are appraised.

17. Apart from all this, the university will offer a course of "Innovative Qualities, " for which President Zhu Qingshi will in person lecture on "How Did Galois Invent Group Theory."

18. According to algebraic property that a direct sum of Galois fields is isomorphic to a finite ring, the linear block code for multiplexing systems is proposed.

19. The main means used in the paper are group theory, galois field, module algebra and linear algebra.

20. Modular inversion is a part of the kernel for computations in the Galois field GF(p) used by many public key cryptosystems.

21. Long standing questions about compass and straightedge construction were finally settled by Galois theory.

22. On this basis, we analyse the performance of the system applying Galois Field Network Coding as well as Complex Field Network Coding.

23. I was not able to bring my un-ease into focus, to get hold of it, find words for it, until I had finished their book on Galois and the Theory of Groups.

24. The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product .