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

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Jonathan George
Jonathan George 2022 年 12 月 8 日
回答済み: Sai 2022 年 12 月 30 日
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?

回答 (1 件)

Sai
Sai 2022 年 12 月 30 日
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

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