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...80. 63. Tim Hsu, Class 2 Moufang loops small Frattini Moufang loops and code loops, (1996). http://lanl.arxiv.org/pdf/math.GR/9611214 64. Vasan...

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...This book has four chapters. In chapter one we just recall the notion of RD codes, MRD codes, circulant rank codes and constant rank codes and describe their properties. In chapter two we introduce few new classes of codes and study some of their properties. In this chapter we introduce the notion of...

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...Preface 5 Chapter One BASIC PROPERTIES OF RANK DISTANCE CODES 7 Chapter Two RANK DISTANCE BICODES AND THEIR PROPERTIES 25 Chapter Three RANK DISTANCE m-CODES 77 Chapter Four APPLICATIONS OF RANK DISTANCE m-CODES 131 FURTHER READING 133 INDEX 144 ABOUT THE AUTHORS 150...

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...ency, we just state here how they are used in developing error correcting codes, as codes which can correct errors is always desirable than codes whi... ... near-rings to automatons and the use of binear-rings to error correcting codes. DEFINITION 8.3.1: Let (N, +, ) be a non-empty set we say N is a b... ... Now we see the probable applications of binear-rings to error correcting codes and their Smarandache analogue. The study of how experiments can... ...fficiency; we just state how they are used in developing error correcting codes as codes which can correct errors is always desirable than the ones ... ... is group forming. Now how are they used in obtaining error correcting codes. Now using the planar near-ring one can construct a BIBD. By taking ... ...ns of the incidence matrix of such a BIBD one can obtain error correcting codes with several nice features. Now instead of using a planar near-ring ... ...g S-planar near-rings will even prove to be an efficient error correcting codes. Now we give the binear-ring analog of it. DEFINITION 8.3.38: ... ...biplanar binear-rings will even prove to be an efficient error correcting codes. PROBLEMS: 1. Give an example of a ring loop. 2. Let (N = Q ∪ ...

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...ional sequences and the locations of those changes are pointed out in the code. Note on programs: All of the C++ programs appearing in this book wer... ... extension *cpp so the compiler treated them as C+-"- files even when the code is essentially C. 25 The other programs were written in L"BASIC veL...

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..., 163, 197] 85. Schitkowski, K., More Test Examples for Non-linear Programming Codes, Lecture Notes in Economics and Mathematical Systems: 282, Spr...

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......................15 The computer coding misused in Computer Science ...................15 Codification problems ..............................17 Codes misclassification .............................18 Chapter 3 ..................................21 Miscomputing the time for creating an application misusing the mudflow scrambles ........21 Misinformation deregistrati...

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... THEOREM [27]: An F-subset A ∈ F(X ∗ ) of the free monoid X ∗ is an F-code over X if and only if for all n, m ≥ 1 and x 1 , …, x n , x' 1 , …, x... ...proof is left for the reader. THEOREM 1.10.27: Let A ∈ F(X + ) be an F-code. Let y ∈ X ∗ be an unordered word such that X ∗ yX ∗ ∩ X ∗ = φ. Le... ...X ∗ – A ∗ – X ∗ yX ∗ . Then the F-set B = A ∪ y(Uy) ∗ is an F-complete code. THEOREM 1.10.28: Any maximal F-code is F-complete. Proof: Let... ...0.28: Any maximal F-code is F-complete. Proof: Let A ∈ F(X + ) be an F-code, which is not F-complete. If card (X) = 1, then A = φ and A is not ma... ...icts the fact that u ∈ ) A ( F * 0 . It follows that A ∪ {(y, 1)} is an F-code and A is not a maximal F- code. Now we recall the concept of λ-thi... ...1, 2, …, n – 1 . Now A i ⊂ X i (X n – w) ∗ . Since X n – w is an F-code, we have Π f [(X n – w) ∗ ] = () () k 0 k n j w X ∑ ≥ − Π = () ... ...− = Π 1 n 0 i i f A = . ) w ( 1 f ∞ < Π THEOREM 1.10.35: Let A be an F-code over X. Then A is F-complete if and only if A is F-dense or maximal. ... ...ected to prove. THEOREM 1.10.36: Let A ∈ F(X ∗ ) be a finite maximal F-code. For any non-empty subset Y of X, the F-code A ∩ Y ∗ is a maximal F-... ...(a n ) > 0. Proof: Refer [72]. THEOREM 1.10.37: Let A be an F-thin code. The following conditions are equivalent. i. A is a maximal F-code...

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...irst section, we analyze the evils of untouchability due to Hinduism and its codes. In section two, the discrimination faced by Dalits and Sudras i... ... R 1 – Religion By the term ‘religion’ the expert refers to the social codes and spiritual activities one is supposed to follow by belonging... ...ry complicated. So we took the 66 links and worked with it using the pseudo code in C language [69, 76]. The data given by her was fed in the for... ...Hindu/ Brahmin public and government S 13 - Untouchability S 14 - Legal codes of the Varnashrama Dharma These attributes were defined as the... ... vector. Consider T = (0 0 0 0 0 0 0 0 0 0 0 0 0 1) i.e., where the node, ‘Code of Varnashrama Dharma’ alone is in the ON state and all other nod... ...d not get educated; if the low castes get educated in spite of the religious codes their tongue should be cut off; if they hear slokas, molten lead... ...ould not interfere in 146 religious matters. Common man fears the religious codes and shuns any reformation. Having faith in religion, if one wis... ...vernment order, and to walk in the public streets you need a law in the Penal code. Is it possible for you to go to walk into the agraharam (Brahmin... ...cted. Each caste should protect its ethics and have the right to practice its codes and customs; it also guarantees them that it will protect such ...

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..., 101010, 11111111, 1212121212, 202020202020, 21212121212121, . . . The code of listing 4 will generate the elements of the Natural Sequence for th...

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..., 163, 197] 85. Schitkowski, K., More Test Examples for Non-linear Programming Codes, Lecture Notes in Economics and Mathematical Systems: 282, Spr...

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...nd Geometries, 5, 297-304 (1988). 11. CHEIN, Orin and GOODAIRE, Edgar G., Code loops are RA2- loops, J. Algebra, 130, 385-387 (1990). 12. CHEIN, Or...

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...In this book the authors study the erasure techniques in concatenated Maximum Rank Distance (MRD) codes. The authors for the first time in this book introduce the new notion of concatenation of MRD codes with binary codes, where we take the outer code as the RD code and the binary code as the inner code....

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...understood by a beginner. Binary symmetric channel is an illustration of a model for a transmission channel. Now we will proceed onto define a linear code algebraically....

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...Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two ALGEBRAIC LINEAR CODES AND THEIR PROPERTIES 29 Chapter Three ERASURE DECODING OF MAXIMUM RANK DISTANCE CODES 49 3.1 Introduction 49 3.2 Maximum Rank Distance Codes 51 3.3 Erasure Decoding of MRD Codes 54 Chapter Four MRD CODES –SOME P...

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... . . . . . . . . . . . 115 4.9 筛序列. . . . . . . . . . . . . . . . . . . . . . 116 4.10 Syllabic Puzzle序列. . . . . . . . . . . . . . . . . 118 4.11 Code Puzzle序列. . . . . . . . . . . . . . . . . . 118 4.12 幂序列. . . . . . . . . . . . . . . . . . . . . . 118 4.13 伪阶乘序列. . . . . . . . . . . . . . . . . . . . 119 4.14 伪因子序列. . . . . . . . . . . . . . . . . . . . 120 4.15...

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...Coding may be defined as a mapping of words from a source alphabet A to a code alphabet B. A discrete, finite memory-less channel with finite inputs... ...ty that for an input letter i output letter j will be received. A code word of length n is defined as a sequence of n input letters, which ar... ...nput letters, which are actually n integers chosen from 1, 2 … a. A block code of length n having M words is a mapping of the message integers from ... ...ng M words is a mapping of the message integers from 1 to M into a set of code words each having a fixed length n. Thus for a structured product wi... ...length n. Thus for a structured product with N component assets, a block code of length n having N words would be used to map message integers from... ... corresponding to 81 each of the N assets, into a set of a fixed-length code words. Then there would be a total number of C = 2 N possible combin... ...ses (flip- flops) would be needed. A decoding system for a block code is the inverse mapping of all output words of length n into the origi... ...s are used with same probability 1/M, the probability of error P e for a code and decoding system ensemble is defined as the probability of an inte... ...quality we have K = Σ n 2 –li ≤ 1, where l i stands for some definite code word lengths with a radix of 2 for binary encoding. For block codes, l...

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...is a bicode with some mathematical structure. In many cases as in case of codes the mathematical structure of a bicodes refers to the fact that it ... ... bicode over Z p . Thus a bicode can also be defined as a ‘union’ of two codes C 1 and C 2 where union is just the symbol. For example we can ha... ...1 1 1), (0 1 0 1), (0 0 1 0), (1 1 0 0), (1 0 1 1)} over Z 2 . These codes are subbispaces of the bivector space over Z 2 of dimension (6, 4)... ...ode if and only if both C 1 (n 1 , k 1 ) and C 2 (n 2 , k 2 ) are linear codes of length n 1 and n 2 with k 1 and k 2 message symbols respecti... ...bicode over Z 2 . Now the main advantage of a bicode is that at a time two codes of same length or of different length are sent simultaneously and t... ...are sent simultaneously and the resultant can be got. 116 As in case of codes if x = x 1 ∪ x 2 is a sent message and y = y 1 ∪ y 2 is a recei... ...∪ C 2 (n 2 , k 2 ) a bicode over Z 2 where C 1 (n 1 , k 1 ) is a (7, 4) code and C 2 (n 2 , k 2 ) is a (9, 3) code given by the generator bimatr... ... a C (n, k) = C 1 (6, 3) ∪ C 2 (4, 2) bicode over Z 2 . The 2 3 ∪ 2 2 code words x 1 and x 2 of the binary bicode can be found using the gene... ...ne cyclic bicodes. So we define a cyclic bicode as the union of two cyclic codes for we know if C (n, k) is a cyclic code then if (x 1 …x n ) ∈ C (n...

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...language and with strict separation of data (called: "structures") and instruction code (called: "functions" or "procedures"). The machine language... ... in saying that it is "intelligent" or has a mental life. But – if it possesses the codes and the instructions – it could make independent use of th... ...re general antitrust/competition law. GATT, though, has an International Antitrust Code Writing Group which produced a "Draft International Antitr... ...matters. The United Nations Conference on Restrictive Business Practices adopted a code of conduct in 1979/1980 that was later integrated as a U.N.... ...inuum, or spectrum. Yet, this may be a simplistic view, indeed. Simple procedures (codes, programs), in nature as well as in computing, often yield... ...d acts. The average Babylonian could have memorizes and assimilated the Hammurabic code 37 centuries ago - it was short, simple, and intuitively ju... ...cisions, collectively known as "case law". Despite the publishing of a Model Penal Code in 1962 by the American Law Institute, the criminal provisi... ... fraction of his country's fiendishly complex and hopelessly brobdignagian criminal code. Such inevitable ignorance breeds criminal behaviour - some... ...y, unencumbered by a past of transgressions against an inane and inflationary penal code. This, admittedly, will reduce the leverage the state has ...

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...information technology. Both markets are founded on the manipulation of symbols and coded concepts. The dynamic of these markets is self-reinforcing... ...ion making procedure. An outside agency, which enforces cooperation and some moral code, is such a decision making procedure. It is not an "outside... ...re companies (which did not). Recently, Netscape has decided to provide its source code (the most important commercial secret of any software comp... ...rs like corruption, civil rights, the composition of the media, the penal and civil codes, environmental policies, or the allocation of economic res... ...Economist", that the Red Cross felt compelled to draw up a ten point mandatory NGO code of ethics. A code of conduct was adopted in 1995. But the p... ...a state of mind. It is an all- encompassing, holistic, worldview, a set of values, a code of conduct, a list of goals, aspirations, fantasies and pr... ...g", "protocol", "agreement" are all legal terms. Standards, protocols, behavioural codes - whether voluntarily adopted or not - are all form of Law... ... and software prevent render certain content inaccessible. The scientific method (a codex) is part of every technological advance. Microchips incorp... ... of monopolists release hitherto monopolized information (for instance, the source codes of software) to the public and increases competition - the...

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...engers, the total collection and the occupancy rate. THE JAVA PSEUDO CODE TO EVALUATE THE FIXED POINTS FOR CLAMPED VECTORS import java.apple... ...tee’s argument is linear and based on a literal reading of the Bankruptcy Code. As a simple FCM, eight nodes arranged in four layers can describe the... ...editor (T4). The third layer of the trustee’s FCM incorporates Bankruptcy Code provisions to reach intermediate inferences: 101 (30) (B) (ii) transf... ... The third layer suppose that a benefit equals a transfer and it uses the Code to determine if the resulting individual transfers are “avoidable”. Ac...

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...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 co...

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...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 fun...

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...rödinger Equation and Quantization of Celestial Systems 67 Epilogue 76 Acknowledgment 78 References 79 Appendix I: An example of self-referential code 88 Appendix 2: Summary of bibliography of Non-Standard Logic 93 Appendix 3: List of some known paradoxes 95 Appendix 4: A few basic notations 103 Appendix 5: A few historical achievements in foundation of set theory ...

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...Monotone Boolean functions . . . . 40 2.4.3 Generation of MBF . . . . 42 2.5 Conclusion . . . . . 45 2.6 References . . . . . 46 Appendix: MatLab code for generating hyper-power sets . . . 48 3 Partial ordering on hyper-power sets 49 3.1 Introduction to matrix calculus for belief functions . . . 49 3.2 Ordering elements of hyper-power set for matrix calculus . . . ...

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... 226 7.3.6 Generation of DΘ r . . . . . . . 230 7.3.7 Decoding . . . . . . . . . 231 7.4 Concluding remarks . . . . . . . . . 232 7.5 MATLABTM codes . . . . . . . . . 233 7.5.1 Codification . . . . . . . . . 238 7.5.2 Combination . . . . . . . . . 243 7.5.3 Decision . . . . . . . . . 250 7.5.4 Decoding and generation of DΘ r . . . . . . 264 7.6 Acknowledgment...