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What is the remainder obtained by dividing $x^7 + x ^5 + 1$ by the generator polynomial $x^ 3 + 1?$
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$x^3+1=1*x^3+0*x^2+0*x^1+1*x^0$

Generator Polynomial=1001

So we've to append three 0s at the end of the message

message=$x^7+x^5+x^1=1*x^7+0*x^6+1*x^5+0*x^4+0*x^3+0*x^2+0*x^1+1*x^0$

=10100001

Remainder=$0*x^3+1*x^2+1*x^1+1*x^1$

=$x^2+x+1$

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