A Short Course on Error Correcting Codes by N.J.A. Sloane

By N.J.A. Sloane

Show description

Read or Download A Short Course on Error Correcting Codes PDF

Similar computer science books

An Introduction to Formal Languages and Automata (3rd Edition)

An advent to Formal Languages and Automata offers a superb presentation of the cloth that's necessary to an introductory idea of computation path. The textual content was once designed to familiarize scholars with the rules and ideas of computing device technological know-how and to bolster the students' skill to hold out formal and rigorous mathematical argument.

Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications

Genetic Algorithms and Genetic Programming: smooth ideas and useful functions discusses algorithmic advancements within the context of genetic algorithms (GAs) and genetic programming (GP). It applies the algorithms to major combinatorial optimization difficulties and describes constitution id utilizing HeuristicLab as a platform for set of rules development.

The ebook makes a speciality of either theoretical and empirical facets. The theoretical sections discover the real and attribute homes of the elemental GA in addition to major features of the chosen algorithmic extensions built by way of the authors. within the empirical components of the textual content, the authors follow fuel to 2 combinatorial optimization difficulties: the touring salesman and capacitated car routing difficulties. to focus on the houses of the algorithmic measures within the box of GP, they research GP-based nonlinear constitution id utilized to time sequence and class difficulties.

Written via center participants of the HeuristicLab workforce, this ebook presents a greater realizing of the fundamental workflow of gasoline and GP, encouraging readers to set up new bionic, problem-independent theoretical suggestions. by way of evaluating the result of common GA and GP implementation with a number of algorithmic extensions, it additionally exhibits tips on how to considerably elevate a possibility answer quality.

Platform Ecosystems: Aligning Architecture, Governance, and Strategy

Platform Ecosystems is a hands-on consultant that provides an entire roadmap for designing and orchestrating vivid software program platform ecosystems. in contrast to software program items which are controlled, the evolution of ecosystems and their myriad contributors needs to be orchestrated via a considerate alignment of structure and governance.

Classical And Quantum Computing With C++ And Java Simulations

[i\Classical and Quantum Computing[/i] presents a self-contained, systematic and complete advent to all of the matters and methods very important in medical computing. the fashion and presentation are effortlessly available to undergraduates and graduates. lots of examples, observed by way of whole C++ and Java code anyplace attainable, conceal each subject.

Extra resources for A Short Course on Error Correcting Codes

Sample text

40 + 5 = 125 in the two cases. To summarize: First Coordinate not in error Number of Errors 1n error 1 253 77 2 176 112 3 141 125 Therefore there is a simple threshold test: if more than 133 out of the 253 parity checks fail, the first coordinate is in error, if less than 133 fail this coordinate is correct. This test can then be applied successively to all the coordinates (using the fact that thc code is invariant under a transitive group ). § 3. 2) For the use of the weight enumerator in obtaining properdes of a code, see for example MacWilliams [ 76], Berlekamp [ 1] Ch.

V) To show that ~ is invariant under T: T sends the first row of G into 0,1,0100011101,1,1,0000000000 which is easily verified tobe the sum of rows 0,2,6, 7,8,10,11, and therefore is in the code. T sends the last row of G into 112 d 2 , which is the complement of the last row, and is in the code by (iv). (vi) We divide each vector of ~ into a left half L and a right half R. Clearly wt(L) =wt(R) = 0 (modulo 2). R will denote the complement of the right half. (vii) <§ contains no vector of weight 4.

1 02-106. J. D. Thesis, Dept. , Harvard University, May, 1962. L. A. Sloane (1972), Generalizations of Gleason's Theorem on Weight Enumerators of Self-Dual Codes, PGIT 18:794-805. L. A. Sloane (1973), An Upper Bound for Self-Dual Codes, IC 22: 188-200. L. A. Sloane (197 ), On the Invariants of a Linear Group of Order 336, Proc. Camb. Phil. , To Appear. F. E. Y. 1961. 58 References [ 88] Molien, T. (1897), Ueber die Invarianten der Linear Substitutionsgruppen, Sitzungsber. Koenig. Preuss. Akad. , pp.

Download PDF sample

Rated 4.72 of 5 – based on 49 votes