Determine the characteristic polynomials of short PN sequences

[SG Kim]

Hello, I'm new to spread spectrum.

i'm trying to make a short PN code in C.
but i'm wondering how determine the characteristic polynomial in short PN codes.

short pn code's characteristic polynomials are known as below.
I: P(X)=X15 + X13 + X9 + X8 + X7 + X5 + 1
Q(X)=X15 + X12 + X11 + X10 + X6 + X5 + X4 + X3 + 1

so, the problem is WHO make that polynomials?

if i want to use 5 registers in LFSR,
how to make a characteristic polynomial?

my english is no good for reading.
i'm not good at english, but please help.

 

[FvM]

For maximum length LFSR polynominals, see Linear feedback shift register - Wikipedia, the free encyclopedia

If you want other than maximum length PN codes, you should tell a specification first.