5) Consider a code with block length n=7. For the polynomial X'+1 find all the factors.To generate a (7, 4) cyclic code, take x3 +x2 +1 as a generator polynomial and findall the codewords.

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Answered: 5) Consider a code with block length…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 56E

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Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .
a. Excluding the identity cipher, how many different translation ciphers are there using an alphabet of n "letters"? b. Excluding the identity cipher, how many different affine ciphers are there using an alphabet of n "letters," where n is a prime?

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5) Consider a code with block length n=7. For the polynomial X+1 find all the factors. To generate a (7, 4) cyclic code, take x3 +x2 +1 as a generator polynomial and find all the codewords.