Finding the generator matrix for x^3+x+1

Hello, I'm inexperienced with MATHLAB and just trying to handle the ropes.

I have managed to use

genpoly=[1 1 0 1];

[parmat,genmat]=cyclgen(7,genpoly,'nonsys')

[parmatsys,genmatsys]=cyclgen(7,genpoly)

to construct a generator matrix for the g( x ) =x^3+ x^2+1 polynominal with (7,4) cyclic code but I'm having difficulty using the same method to find the generator matrix for x^3+x+1. Could someone please help me out with an astute explanation so I may understand it better?

Answer 1

[Sai]

Hi Jonathan,

Let g(x) be generator polynomial.

If g(x) = x^3 + x + 1 = 1 + x + x^3 is a generator polynomial, then the corresponding generator polynomial vector(genpoly) would be [1 1 0 1] but not [1 0 1 1]. In that case, for g(x) = x^3 + x^2 + 1, then genpoly would be [1 0 1 1] but not [1 1 0 1]. ‘genpoly’ is obtained from g(x) considering g(x) is written in increasing powers of x.

The following code snippet helps you finding generator matrix for g(x) = x^3 + x^2 + 1 = 1 + x^2 + x^3

genpoly=[1 0 1 1];
[parmat,genmat]=cyclgen(7,genpoly,'nonsys')
[parmatsys,genmatsys]=cyclgen(7,genpoly,'system')

The following code snippet helps you finding generator matrix for g(x) = x^3 + x + 1 = 1 + x + x^3

genpoly=[1 1 0 1];
[parmat,genmat]=cyclgen(7,genpoly,'nonsys')
[parmatsys,genmatsys]=cyclgen(7,genpoly)

Hope the query is resolved