polynomial division issue, how to find the remainder

i have two polynomials like

a=X14 + X13 + X10 + X9

b=X8 + X7 + X6 + X4 + 1

i want to find a mod b using matlab pls.

[Walter Roberson]

Are these binary polynomials?

Is X14 related to X^14 ?

[aya]

yes x4=x^4 and so on

[aya]

hello sir i am really thankful for your help but i still have problem with polynomial remainder that is what i am doing

a='110011000000000'; aa=bin2dec(a); b='000000111010001'; bb=bin2dec(b); r=rem(aa,bb); re=dec2bin(r)

re =

1001000

the answer re should be 1001 why i am getting these extra zeros by the way a=x^14+x^13+x^10+x^9 and b=x^8+x^7+x^6+x^4+1

another thing when i write them with out making them have the same size i get a totaly different answer

Answer 1

[Roger Stafford]

If your field is that of the real numbers, look at 'deconv' function at:

 http://www.mathworks.com/help/matlab/ref/deconv.html

This is a quote from that documentation: "If u and v are vectors of polynomial coefficients, convolving them is equivalent to multiplying the two polynomials, and deconvolution is polynomial division. The result of dividing v by u is quotient q and remainder r."

[aya]

sir now i have another problem that is i have a streem c=110001111101010 i want to convert it to -1 for 1 and 1 for 0 how can i do that since c elemnts dose not have an index just like matrices

[Walter Roberson]

What datatype is c ? Do you mean c = [1 1 0 0 0 1 1 1 ...] or do you mean c = '1100011...' or do you mean c=110001111101010 decimal ?

[aya]

c='110001111101010'

Answer 2

[Walter Roberson]

Possibly x^6 + x^3 depending on what your formulae mean.

[aya]

sir i just want to divide the first polynomial by the second one and find the reminder , is there any way to do that?

[Walter Roberson]

Well this gets into a bit of Math theory, which I won't explain here (because I do not remember it.)

When you have polynomials whose coefficients are all 0 or 1, then to find the mod, convert both of them into binary numbers, convert the binary into decimal (numeric) form, take the mod of the numeric form, convert the numeric form back into binary, convert that to polynomial notation.

For example,

x^5 + X^3 + X^2 + 1 maps to binary [1 0 1 1 0 1], which is decimal 45
x^3 + X             maps to binary [1 0 1 0], which is decimal 10
45 mod 10 is 5
5 in binary is [1 0 1]
in polynomial form that is X^2 + 1
so (x^5 + X^3 + X^2 + 1) mod (x^3 + X) is (X^2 + 1)

[aya]

how to convert binary to decimal

if i have a=rand(1,8)>0.5

aa=bin2dec(a) an error will occur tells that a must be string????

[aya]

"a" must be string*

[Walter Roberson]

aa = bin2dec(char(a + '0'));

[Walter Roberson]

To convert c='110001111101010' to -1 for 1 and 1 for 0, use

2*('0' - c) + 1

Answer 3

[M Naeem]

how we divide two polynomials in Polynomial Ring (Z_2[x]) to find the remainde?... let suppose i want to divide x^113 by x^8+x^4+x^3+x^2+1