What are the zeros of polynomials arising in coding theory (e.g., generator polynomials of cyclic codes)? Roots in extension fields and their relation to the code's properties (minimum distance)

Do you want to go back to the question? Submit Go back. Learn with an example. Match each polynomial function to its graph. f. Apr 3, 2024 ... 39 votes, 22 comments. To possibly go into the question in more detail: If a polynomial function does not have a constant, we can at least ... Oct 6, 2021 ... The Factor Theorem is another theorem that helps us analyze polynomial equations. It tells us how the zeros of a polynomial are related to the factors. This lesson highlights a variety of tools for writing polynomial functions and solving polynomial equations. In general, if a function f ‍ has a zero of odd multiplicity, the graph of y = f ( x ) ‍ will cross the x ‍ -axis at that x ‍ value. If a function f ‍ has a ... Every Polynomial Equation with a degree higher than zero has at least one root in the set of Complex Numbers. A Polynomial Equation of the form P(x) = 0 of ... Nov 16, 2022 ... We say that x=r x = r is a root or zero of a polynomial, P(x) P ( x ) , if P(r)=0 P ( r ) = 0 . In other words, x=r ... There are three theorems and a rule that we will be referring to during this lesson in order to help make the discovery of the roots of polynomial functions ... May 21, 2012 ... The zeros of a function are the values of the input to the function that make the output equal to zero. The zeros of a polynomial function are ... Mar 4, 2022 ... Zeros of a polynomial are the values of \(x\) for which the polynomial equals zero. In other words, they are the solutions of the equation ...