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Scientia Magna : An International Journal : Volume 3, No. 2, 2007

By Xi'an, Shaanxi

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Book Id: WPLBN0002828574
Format Type: PDF eBook:
File Size: 3.42 MB
Reproduction Date: 8/7/2013

Title: Scientia Magna : An International Journal : Volume 3, No. 2, 2007  
Author: Xi'an, Shaanxi
Volume: Volume 3, No. 2, 2007
Language: English
Subject: Non Fiction, Science, Algebra
Collections: Authors Community, Mathematics
Publication Date:
Publisher: World Public Library
Member Page: Florentin Smarandache


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Xi'anitor, B. S. (Ed.). (2013). Scientia Magna : An International Journal : Volume 3, No. 2, 2007. Retrieved from

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

Abstract In this paper, we use 4-cyclotomic cosets of modulo n and generator polynomials to describe quaternary simple-root cyclic codes of length n = 85. We discuss the conditions under which a quaternary cyclic codes contain its dual, and obtain some quantum error-correcting codes of length n = 85, three of these codes are better than previous known codes. Keywords Quaternary cyclic code, self-orthogonal code, quantum error-correcting code. x1. Introduction Since the initial discovery of quantum error-correcting codes, researchers have made great progress in developing quantum error-correcting codes. Many code construction are given. Reference [1] gives a thorough discussion of the principles of quantum coding theory. Many good quantum error-correcting codes were constructed from BCH codes, Reed-Muller codes, Reed-Solomon codes and algebraic geometric codes, see [2-6]. So it is natural to construct quantum error-correcting codes from quaternary cyclic codes. It is known that there is a close relation between cyclotomic coset and cyclic codes. Suggested by this relation, we use 4-cyclotomic coset modulo n and generator polynomials to describe self-orthogonal cyclic codes and their dual codes. This paper is organized as follows. In this section, we introduce some definition and do some preparation for further discussion. In section 2, we construct quaternary cyclic codes of length 85 and related quantum error-correcting codes. In section 3, we compare the parameters of our quantum error-correcting codes and related cyclic codes with previously known.

Table of Contents
S. M. Khairnar and M. More : Subclass of analytic and univalent functions in the unit disk 1 Y. Ma, etc. : Large quaternary cyclic codes of length 85 and related quantum error-correcting 9 J. Chen : Value distribution of the F.Smarandache LCM function 15 M. Bencze : About a chain of inequalities 19 C. Tian and N. Yuan : On the Smarandache LCM dual function 25 J. Caltenco, etc. : Riemannian 4-spaces of class two 29 Y. Xue : On a conjecture involving the function SL¤(n) 41 Y. Wang : Some identities involving the near pseudo Smarandache function 44 A. Gilani and B. Waphare : On pseudo a-ideal of pseudo-BCI algebras 50 J. Chen : An equation involving the F.Smarandache multiplicative function 60 M. Enciso-Aguilar, etc. : Matrix elements for the morse and coulomb interactions 66 Y. Xu and S. Li : On s¤¡Supplemented Subgroups of Finite Groups 73 C. Tian : Two equations involving the Smarandache LCM dual function 80 W. Zheng and J. Dou : Periodic solutions of impulsive periodic Competitor- Competitor-Mutualist system 86 X. Zhang : On the fourth power mean value of B(Â) 93 Z. Lv : On the F.Smarandache function and its mean value 104 J. Ge : Mean value of F. Smarandache LCM function 109


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