Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let g(x) be a polynomial in Z₂[x]. Prove that if the polynomial code C generated by g(x) with length n is cyclic, then g(x) is a factor of x + 1 in Z₂[x].

Let g(x) be a polynomial in Z₂[x]. Prove that if the polynomial code C generated by g(x) with length n is cyclic, then g(x) is a factor of x + 1 in Z₂[x].

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.1: Polynomial Functions Of Degree Greater Than
Problem 36E
See similar textbooks
icon
Related questions
Question
13. Let g(x) be a polynomial in Z₂[x]. Prove that if the polynomial code C generated by g(x) with length n is cyclic, then g(x) is a factor of x" + 1 in Z₂[x].
Transcribed Image Text:13. Let g(x) be a polynomial in Z₂[x]. Prove that if the polynomial code C generated by g(x) with length n is cyclic, then g(x) is a factor of x" + 1 in Z₂[x].
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS