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Primitive Elements -> the basic element from which all other elements of the field can be obtained by exponentiation. i.e., an element A of the field in which the element B is a primitive element can be written as B = A ^n, where n is some non-negative integer. Be aware that the law of exponentiation (multplication) is not the same as that for integers. In GF(2^4) α = 0010 is primitve element
Primitive Polynomials -> are unfactorizable polynomial in the base field, whose root is the primitive element. a primitve poly : α^4 + α^2 + 1. this poly cannot be factorised in GF(2) (i.e., 0 and 1 arent roots), it also the such smallest degree poly with α as root.
-b
Not very clear what the question is. If it is "why you need to know this". It is because it is the basis for understanding BCH/Reed Solomon decoding later.
This view was useful for me:
The decoding algorithms can be understood with usual algebra. However, the operations like add, mul are "redefined" in this algebra. These definitions and terms are introducing this new algebra to you.
As an example: You very well know how to multiply two polynomials. whats the difference here? The coefficients of the poly here are the field elements (generated by the primitive poly). When you multiply the polys, as usual, you add up the product of coefficients which give same degree, but here you use the GF definition of multiplication and addition while doing this. The GF multiplication rule evolves from the primitive poly.
HTH
-b
i need the following questions to be resolved, how to generate primitive polynamials, minimal polynamials,
For that if posssible for you I need your email so that I can get the answer thru voice chat if possible for you, i have wasted a lot of time in that
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