Syndrome Now if the data read has 3 errors, such as r(x) = (100100100101011), the syndrome can be found from the followi

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Syndrome Now If The Data Read Has 3 Errors Such As R X 100100100101011 The Syndrome Can Be Found From The Followi 1 (54 KiB) Viewed 58 times

how to solve s1(a)=a^12?

Syndrome Now If The Data Read Has 3 Errors Such As R X 100100100101011 The Syndrome Can Be Found From The Followi 2 (47.35 KiB) Viewed 58 times

I want to how to get a^12

Syndrome Now If The Data Read Has 3 Errors Such As R X 100100100101011 The Syndrome Can Be Found From The Followi 3 (137.02 KiB) Viewed 58 times

Syndrome Now if the data read has 3 errors, such as r(x) = (100100100101011), the syndrome can be found from the following equations. Due to t= 3, we have 2t = 6 syndrome elements needed in order to find t errors.
S(x) = r(x) mod f(x) sz(x) = r(x) mod f(x) = r(x) mod f(x) Sz(x) = r(x) mod f(x) S4(x) = r(x) mod f(x) = r(x) mod f(x) S5(x) = r(x) mod f5(x) 56(x) = r(x) mod f.(x) = r(x) mod f3(x)
In selecting the minimal polynomials, we take advantage of the property of field elements whereby several powers of the generating element have the same minimal polynomial. When f(x) is a polynomial over GF(2), a is an element of GF(2"). Then we form a system of equations in a as follows: S(a) = r(a) mod f(a) = a + ( + a + 1 = a12 szl(?) = r(a) mod f((?) = r(a) mod f,(a?) = q* + a = sz(a) = r(a) mod f(a) = a + (n + a2 + 1 92 s.(a*) = r(a) mod f.(a) = r(a) mod f,(a") = a?? + a + q* + 1 € C3 Ss(as) = r(a) mod f(a) = 5 so(aa) = r(a) mod fo(aº) = r(a) mod f3(aº) = a18 + a?? + d + 1 aº