modulo 4 two polynomials multiplication

[Aya2002]

Hi Friends,

would somebody help me please as i think there is an error in the book.

Please I need the result of multiplying the following two polynomials as a modulo 4 multiplication:

f(x)=1+2x+3x^2
g(x)=3+x+2x^2+x^3

The results in the book was 3 + 3x + x^2 + 3x^3 is this result correct?

this example was in page 53 of NON-BINARY ERROR CONTROL CODING FOR WIRELESS COMMUNICATION AND DATA STORAGE
by Rolando Antonio Carrasco and Martin Johnston
first published 2008

Thank you too much.

 

[Aya2002]

any comment please?

 

[puripong]

I think the corrected result is
3 + 3x + x^2 + 3x^5

Are you agree with me ?


ps. I would like to read this book

 

[_Eduardo_]

This is a copy of the page 53

**broken link removed**

In all steps the last power must be x^5 rather than x^3



The book can be found at rapidshare,depositfiles...

 

[puripong]

I will get it there , thanks

 

[Aya2002]

I think the corrected result is
3 + 3x + x^2 + 3x^5

Are you agree with me ?


ps. I would like to read this book

but in modulo - 4 the power of x = 5 is not possible so it will be x to the power 1 then the final result will be

3 + 6x + x^2

is this answer correct?

 

[zorro]

but in modulo - 4 the power of x = 5 is not possible so it will be x to the power 1 then the final result will be

3 + 6x + x^2

is this answer correct?

No. Modulo arithmetic applies to coefficients, not to powers.
Regards

Z

 

[puripong]

I think so.

but in modulo - 4 the power of x = 5 is not possible so it will be x to the power 1 then the final result will be

3 + 6x + x^2

is this answer correct?

No. Modulo arithmetic applies to coefficients, not to powers.
Regards

Z

 

[Aya2002]

No. Modulo arithmetic applies to coefficients, not to powers.
Regards

Z

would you prove that please. I need it too much

thanks

 

[zorro]

Ha Aya,

Sorry, I saw your message just now.
Powers in the indeterminate variable of the polynomial (let's continue to use "x" for it) indicates position of the accompanying coefficients in a vector. Their meaning is different to that of coefficients, and the way to operate with them too.
For example, the polynomial 3+3x+x^2+3x^5 (over the set of coefficients modulo 4) is a convenient way to express the vector (3,3,1,0,0,3), if we write it in increasing powers [many times the reverse order is used]. A vector of N symbols requires polynomials up to degree N-1. No modulo arithmetic is involved in this.
The good thing about using polynomials is that many operations are readily carried out using usual polynomial theory (multilication, division, remainders).
Regards

Z