A first course in coding theory by Raymond Hill

By Raymond Hill

Algebraic coding conception is a brand new and swiftly constructing topic, well known for its many sensible purposes and for its fascinatingly wealthy mathematical constitution. This ebook offers an uncomplicated but rigorous creation to the idea of error-correcting codes. in line with classes given by means of the writer over a number of years to complex undergraduates and first-year graduated scholars, this consultant encompasses a huge variety of workouts, all with options, making the booklet hugely compatible for person research

Show description

Read or Download A first course in coding theory PDF

Similar machine theory books

Abstract Algebra: Structure and Application

This article seeks to generate curiosity in summary algebra by means of introducing each one new constitution and subject through a real-world software. The down-to-earth presentation is on the market to a readership without previous wisdom of summary algebra. scholars are resulted in algebraic techniques and questions in a typical approach via their daily reviews.

Theoretical Computer Science: 8th IFIP TC 1/WG 2.2 International Conference, TCS 2014, Rome, Italy, September 1-3, 2014. Proceedings

This publication constitutes the refereed court cases of the eighth FIP WG 2. 2 foreign convention, TCS 2014, held in Rome, Italy, in September 2014. The 26 revised complete papers offered, including invited talks, have been rigorously reviewed and chosen from seventy three submissions. [Suggestion--please payment and upload extra if wanted] TCS-2014 consisted of 2 tracks, with separate application committees, which dealt respectively with: - music A: Algorithms, Complexity and versions of Computation, and - song B: common sense, Semantics, Specification and Verification

Duality in Vector Optimization

This ebook provides basics and complete effects relating to duality for scalar, vector and set-valued optimization difficulties in a common surroundings. One bankruptcy is solely consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.

Extra resources for A first course in coding theory

Sample text

Note that by the upper bound proved by [1], our lower bound is actually tight. The Necklace Graph. A D-regular necklace graph N (V, E) with n nodes n units U1 , U2 , . . , U . Each unit Ui for i ∈ [ ] contains D + 1 consists of := D+1 nodes, numbered by 1, 2, . . , D + 1. Within a unit Ui , there is an edge between each pair of nodes except the pair {1, D + 1}. That is, the subgraph of N (V, E) induced by nodes in Ui is KD+1 \1, D + 1. For each i ∈ {1, 2, . . , − 1}, the two units Ui and Ui+1 are connected via an edge between node D + 1 of Ui and node 1 of Ui+1 .

We denote the subgraph constructed by COP with constant parameter D by H, which has diameter d. Hence for any node v, there exists a path P = (u0 , u1 , . . , us−1 , us = v) in the undirected graph induced by H between u0 and v, where s ≤ d is the length of the path. Hence, in the directed graph H, for any i = {0, 1, . . , s − 1}, there is a directed edge between nodes ui and ui+1 . Since both nodes ui and ui+1 have out-degree at most D, which is a constant, communication between ui and ui+1 1 will be performed with probability at least D in each round.

27–38, 2014. c IFIP International Federation for Information Processing 2014 28 F. Chen and X. Wu the neighbor if the neighbor is informed. A common performance measure of protocols is the number of rounds required to have all nodes informed, which is called the finishing time. We consider the rumor spreading problem when the rumor is not a tiny piece of information, but a large file which can not be transmitted from one node to another in one round. In this case, we divide the file into B small pieces so that each piece can be transmitted in one round.

Download PDF sample

A first course in coding theory by Raymond Hill
Rated 4.61 of 5 – based on 43 votes