An irreducible polynomial of degree 8 over GF(2) is given as f(x) =x+x+x'+x +1. This canbe used to define GF(2)=GF(256) which is frequently used to design a code over the ASCIIsymbols consisting of 8 bits.We will use the following notation, for a, e GF(2),e ar + a,r+ ar ++ aa +a,(A) Write a computer program of addition and multiplication for all the binary 8-tuples as aboveand answer to the following questions:(B) Find any member a in GF(256) with the property that a, a², a²̟., a5 are all distinct,Calculate as al28, and a4.ANSWER:) :a binary 8-tuple):a binary 8-tuple):a binary 8-tuple):a binary 8-tuplea = (a4 = (a12 =(ass = ((C) Calculate the multiplications a a, att . atza, and a al0 using your program in (A).Verify, for example, that a at = al+64 = ats, a*. a1zi - att12- al92 etc.(D) Define a linear function g from GF(256) to itself such that g(x) = x for any x in GF(256).Here, the linearity implies that g preserves two operations of the field.That is, for any x,y in GF(256), we haveg(x + y) = g(x) + g(y) and g(x-y) = g(x) - gV).Either prove that g is 1-1 or find a counterexample that g is NOT 1-1.Either prove that g is onto or find a counterexample that g is NOT onto.Report must contain your program source code and the answers to the above three problems.

Answered: Image /qna-images/answer/c20c31bf-1b39-4ee5-8cdb-a22a9ead8718.jpg

Answered: (A) Write a computer program of…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

3. Prof. Poirot needs help. He has a regular expression r and wants to write a regular expression s that generates the the complement of L(r). Can you give him an algorithm for this task? Write it in precise and clear English.
Give a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.
IN PYTHON I want a code in python and no need to post work on paper Iwant a screenshot of the code A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557. The following code format should help: def td(l, m, u, b): '''Solve a linear system Ax = b where A is tridiagonal Inputs: l,…
Describe the following sets by regular expressions, (с) {01, 10} (d) {а, ab}.
Provide a recursive definition for the following set S. S={2k3m5n EN | k, m, n E Z+} Z+ is the set of all positive integers (1, 2, 3, ..) N is a set of numbers so 2^1 * 3^1 * 5^1 = 35 Not in Code format. Base Case and Constructor Case
Write an iterative function that determines the number of even elements in an array a of integers of size n. The function should return the number of elements that are even in array a of size n. Propose an appropriate prototype for your function and then write its code. Write a recursive function to solve the above problem. Propose an appropriate prototype for your function and then write its code.
1.Implement a recursive function allCharsPerm( listOfChars ) the generates all unique permutations of the chars in listOfChars. You can assume listOfChars contains unique chars (no repeated characters in the list). 2.Solve the recurrence and state the time complexity using Big-O notation. This will be challenging. Hint: Try forward or backward iteration / substitution, and keep very organized with your parentheses.
Write a fraction calculator program that adds, subtracts, multiplies, and di-vides fractions. Your program should check for the division by 0, have and use the following functions (a) reduce - reduces a given fraction.(b) flip - reduces a given fraction and flips the sign if the denominator is negative.(c) add - finds the reduced sum of a pair of given fractions.
PYTHON /JUPYTER NOTEBOOKS Program a backward solver (i.e. write your code) for an upper triangular system Ux=b. The algorithm is attached below for Numpy and Python with offset 1. Recall that NumPy and Python have offset 0 for their sequence data types.
Implement a recursive C++ function which takes an array of integers (arr) and the starting (start) and ending (end) indices of a portion (part) of this array, and returns the index of the second smallest element present in that portion of array arr. The prototype of your function should be: int findSecondSmallest (int* arr, int start, int end) For example, the function call findSecondSmallest(arr,3,8) should determine and return the index of the second smallest element present in the array arr between the indices 3 and 8 (both inclusive).
Implement a recursive C++ function which takes an integer array (A) and the starting (start) and ending(end) indices of that array, and returns the sum of all elements present in that array. The prototype ofyour function should be:int findSum (int* A, int start, int end)
(e) Give a simple recursive definition for the function sos(A), which gives the length of the shortest oscillating supersequence of an arbitrary array A of integers.

Recommended textbooks for you

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

C How to Program (8th Edition)

Computer Science

ISBN:

9780133976892

Author:

Paul J. Deitel, Harvey Deitel

Publisher:

PEARSON

Database Systems: Design, Implementation, & Manag…

Computer Science

ISBN:

9781337627900

Author:

Carlos Coronel, Steven Morris

Publisher:

Cengage Learning

Programmable Logic Controllers

Computer Science

ISBN:

9780073373843

Author:

Frank D. Petruzella

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS