Error Correcting Codes A Mathematical Introduction 1st Edition D J. Baylis - Solutions

Discover comprehensive solutions for "Error Correcting Codes: A Mathematical Introduction" by D.J. Baylis. Access our online platform for the complete answers key, featuring detailed solutions pdf and a solution manual. Our expertly solved problems and questions and answers provide a robust test bank with chapter solutions. Enjoy step-by-step answers crafted to help you master each concept, with resources like the instructor manual and textbook guidance. Experience the convenience of a free download, making it easier than ever to navigate this essential mathematical reference.

Develop an application that produces a banner containing information about your project. Items you might include are your programming assignment number, name, date submitted and the purpose of the application. Label each item. These are items you might want to include as internal documentation on
Print your name, school, and the year you plan to graduate. Place your name on one line and your graduation year on the second line. Be sure to include appropriate labels. For example, my information would look like the following, if I planned to graduate in 2017:Name: Barbara Doyle Graduation
First develop a prototype, and then write a program that displays the name of the programming language discussed in this text. You should be more creative, but one possible design is given here. ## CC ## ## ## CC CC #### ## ##
Write a program that produces the following output. Replace the name Tyler Howard with your name.Hello World! My name is Tyler Howard!
Explain the relationship between System, Console, and Read.
Identify the syntax error(s) (if any) in the following:Line 1 using System Line 2 namesspace ExerciseI Line 3 {Line 4 Problem2 Line 5 {Line 6 static Main( )Line 7 {Line 8 console.write("ok")Line 9 }Line 10 }Line 11 }
Using the program segment in Exercise #22, identify line number(s) in which each of the following can be found:a. method invocationb. namespacec. class named. argument to a methode. commentf. identifier
Search the Internet and identify the URL of one site, other than Microsoft, that has a C# compiler available for download.
What must be changed in the segment of code in Exercise #22 to cause all of the output to be displayed on one line?
What is produced when you run the following application?Line 1 // Example program – displaying output.Line 2 using System;Line 3 namespace ExerciseI Line 4 {Line 5 class Problem2 Line 6 {Line 7 static void Main( )Line 8 {Line 9 Console.Write("Go ");Line 10 Console.Write("Laugh ");Line 11
Identify one syntax error that might occur when you type Example 1-1 into an editor.Identify one logic error that might occur.
Which of the following is a call to a method?a. Console.Write;b. Console.Write["ok"];c. Write.Console("ok");d. Console.Write("ok");e. none of the above
Which escape sequence can be used to indicate the cursor should advance to the next line?a. newlineb. escape nextc. d. ewlinee.
To see the results of an application, you the code.a. compileb. JITc. executed. edite. desk check
What is the name of the feature in Visual Studio that displays in a scrollable list all available methods and properties when the dot is typed after an object name?a. Helpb. Rotorc. Monod. IntelliSensee. ToolTip
A(n) is a mock-up of desired output.a. prototypeb. algorithmc. diagramd. specificatione. none of the above
The fully qualified call to the method that allows the user to input a single character is:a. Console.System.Read( )b. System.Console.Read( )c. Console.System.Write( )d. System.Console.Write( )e. System.Console.ReadLine( )
Which of the following is a keyword?a. Main( )b. Systemc. usingd. WriteLinee. all of the above
To mark the beginning and end of a block of code, C# programmers use:a. [ ]b. { }c. ( )d. begin ende. start stop
A(n) groups semantically related types under a single name.a. objectb. classc. methodd. namespacee. directive
System is an example of a(n):a. objectb. classc. methodd. namespacee. directive
Which beginning symbol(s) indicates the following lines will be comments?a. /*b. **c. //d. ///e. */
ASP.NET creates which type of application?a. Windowsb. consolec. commandd. Webe. services
.NET is considered a powerful development environment because:a. It contains over 2000 classes.b. Solutions can be developed using different programming languages.c. Windows applications can be developed easily.d. Component-based development is possible.e. All of the above.
With the object-oriented methodology, the data members are referred to as:a. attributes or characteristicsb. characteristics or behaviorsc. methods or attributesd. behaviors or methodse. attributes or behaviors
After designing your solution, you should before typing any code.a. analyze the problem definitionb. check for run-time errorsc. do maintenance on the solutiond. desk check the solutione. determine what .NET class to use
Cycling back to previous phases as potential problems are uncovered is an example of:a. object-oriented programmingb. stepwise refinementc. Intermediate Languaged. iterative developmente. structured programming
In which phase of the software development process would probing questions be used to verify the problem definition?a. analysisb. designc. codingd. implementatione. testing
The following strategy reduces the amount of time in development and produces more efficient solutions:a. Code the solution as soon as possible.b. Design the solution before coding.c. Analyze the solution before testing and debugging.d. Build a prototype during testing.e. Use a simple, low-level
The program that translates high-level programming language into machine-readable form is a(n):a. applicationb. operating systemc. C# programd. compilere. machine language utility
You run a program and it gives you the difference of two values as the output, instead of the sum of the values, as intended. This is what type of error?a. syntaxb. analysisc. codingd. designe. logic
The Read( ) method accepts any character from a standard input device, such as a keyboard. It does nothing with the character.
One way to document your desired output is to construct a prototype, or mock-up, of your output.
Visual Studio integrated development environment (IDE) is an interactive development environment that enables you to type the source code, compile, and execute without leaving the IDE program.
To see the results of a program, you must type the statements (source code)into a file, compile that code, and then execute the application.
Readability is important. Indenting is not required, but it is a good practice because it makes the code easier to read.
Methods communicate with each other through arguments placed inside parentheses.
WriteLine( ) writes a string message to the monitor or a standard output device.
The keyword void is included to signal that no value is returned. The complete signature of a method starts with the return type, followed by the name of the method, and finally a parenthesized list of arguments. One signature for Main( ) is void static Main( ).
The keyword static indicates that a single copy of the method is created.
The Main( ) method is the entry point for every C# console application. It is the point at which execution begins.
A method is a collection of one or more statements taken together that perform an action. In other words, a method is a small block of code that performs an action.
Everything in C# is designed around a class. Every program must have at least one class.
The using-namespace-directive imports all the types contained in the given namespace. By specifying the namespace around which you are building an application, you can eliminate the need of preceding a class with a dot( . ) and the name of the namespace.
Over 2000 classes make up the Framework class library. A class contains data members and methods or behaviors that can be reused.
It is not necessary to end single inline comments (//); they end when the Enter key is pressed. Comments that span more than one line should be enclosed between /* */. These are considered block or multiline comments.
Comments are written as notes to yourself or to readers of your program.The compiler ignores comments.
All C# programs must define a class.
C# programs usually begin with a comment or using directives, followed by an optional namespace grouping and then the required class definition.
Console applications are the easiest to create. Values can be entered and produced with minimal overhead.
Windows applications are considered desktop bound and designed for a single platform.
Web pages are created using Web forms, which are part of the ASP.NET technology.
C# can be used to create Web, Windows, and console applications.
Originally, development with C# was possible only for the Windows platform; however, a number of projects are in development that are porting C# to other platforms such as Linux.
Through using Visual Studio (which is an IDE) and the .NET Framework classes, C# provides an easy way to create graphical user interfaces.
.NET is a software environment in which programs run. It is not the operating system. It is a layer between the operating system and other applications, providing an easier framework for developing and running code.
C# was designed from scratch to work with the new programming paradigm,.NET, and was the language used for development of much of .NET.
Through inheritance, it is possible to define subclasses of data objects that share some or all of the main class characteristics of their parents or superclasses.Inheritance enables reuse of code.
An object is an instance of a class.
Encapsulation refers to combining attributes and actions or characteristics and behaviors to form a class.
Using an object-oriented analysis approach, the focus is on determining the objects you want to manipulate rather than the logic required to manipulate them.
Software maintenance refers to upgrading or changing applications.
The underlying theme of top-down design or stepwise refinement is that given any problem definition, the logic can be refined by using the divideand-conquer approach.
Procedural programming is process oriented and focuses on the processes that data undergoes from input until meaningful output is produced.
The five problem-solving steps for software development introduced in this chapter include analyzing, designing, coding, implementing, and testing and debugging the solution.
Programming is a process of problem solving. The hardest part is coming up with a plan to solve the problem.
The type of software most often associated with system software is the operating system. The operating system software is loaded when you turn on the computer. Other types of system software are compilers, interpreters, and assemblers.
Software can be divided into two categories: system software and application software. Application software is defined as the programs developed to perform a specific task.
Mobile applications for smart devices today are increasing in demand.
Many consider today’s computer technology to be in the fifth generation of modern computing. Each era is characterized by an important advancement.
The power of the computer rests with software, which is the set of instructions or programs that give the hardware functionality.
1. Try to recover the message with vowels and spaces omitted at the end of section 1.1.
2. The binary 3-fold repetition code is to be used for one of two possible channels. The first is a non-symmetric channel wh ich induces 1 --+ 0 errors with probability a and 0 -+ 1 errors with probability ß. The seeond is asymmetrie ehannel with an overall symbol error probability equivalent to
3. The symbol error prob ability of asymmetrie ehannel is p. The messages are all binary of length 3 and these are eneoded by adding a fourth bit to eaeh message so that the total number of ones in eaeh eodeword is even. What proportion of reeeived words will eontain undetected errors?
1. Encode the messages 1011, 1111 and 0111 using the Hamming (7,4) code.
2. A child's arithmetic homework is sent encoded as a binary string according to the Hamming (7,4) system. The 'messages' are defined be low. Encode the questions: 13 + 49, 259 -7 7, and decode and answer if possible the three questions:00011100000010001110010001111100001000111001
3. Can you prove (preferably not by listing an possible single errors in an sixteen codewords!) that the Hamming (7,4) code will correct an instances of a single error?
4. Using the (8,4) code, encode 1000, 1110, 0011.
5. Decode if possible 11101111, 11010100, 10011100, assuming each word has at most two errors.
6. In the word of the previous exercise found to have two errors, find an the possible error locations.
7. Prove that on the assumption of at most two errors, whenever Hamming(8,4) decoding detects two errors there are always four possible pairs of locations of the errors.
8. The Hamming (7,4) code is used for a channel prone to erasures but not errors. If ?0?0111 is received what was the transmitted word?Show that if ??11001 is received, the 'no errors' assumption cannot be valid. Can the correct word be recovered if the assumption is amended to 'at most one error
9. Show that every word received via the (7,4) channel with two erasures and no errors is uniquely recoverable.
10.(a) Are there any received words with three erasures which the (7,4) code can cope with?(b) Are there any for which it fails?
11. Does your answer to Exercise 10 change if the (8,4) code is used?
12. How many binary strings of length 7 are there?How many of these are codewords of the Hamming (7,4) code?
13. In the geometrie tri angle inequality, why do we have :S and not
14. Prove the triangle inequality for words. That is, if u, v, ware any three words of a code, thend(u, w) :S d(u, v) + d(v, w).
15. How many strings of length n are there if the alphabet has q symbols?
16. What is d( C) if Cis: (a) 3 error-deteeting; (b) 3 error-correeting?
17. C can be used as an a error-deteeting code or as a ß error-correeting code. What are a and ß if: (a) d(C) = 4; (b) d(C) = 5; (c) d(C) = 6?
18. A ternary code (one whose alphabet size is three) C is{cbaaa,bcabc,bacbc,aabbc,acccb,cbbab}.Verify that d(C) = 2, so that by Theorem 2.2 C is not 1 error-correcting.However, this only means that nearest neighbour decoding will not correetalt instances of words received with one error. Find
19. C = {011000, 110110,000011,101101}. Use nearest neighbour decoding to decode, if possible, the following received words: (a) 010110; (b)101101; (c) 110011.
20. Practise the lying game sufficiently to become a professional magician next Christmas!
21. If lying is not allowed is it possible to guess the number with four questions wh ich are independent of the replies received?
1. In section 3.1 we claimed that the 'sum' of any two codewords of the Hamming (7,4) code is another codeword of the same code. Can you think of a way of verifying this without summing all possible pairs of the sixteen codewords?
2. Suppose a = qb + r is a result of dividing a by b. Show that the requirement that the remainder is ::::: 0 and < b makes the values of q and runique.
3. Prove properties i-iv listed in Theorem 3.l.
4. Show from Theorem 3.1 that a :=: b mod m ==> an :=: bn mod m(n 2: 0).How ean this be used to show quiekly that 411220 - 17 Find the remainders when 250 and 4165 are eaeh divided by 7.What is the remainder when L:7~~ i 5 is divided by 4?
5. Show that(a) a:=: b mod m -=f';> ca :=: eb mod m and(b) a2 :=:b2 modm-=f';>a:=:bmodm.

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