When I am reading some algorithm related to error correction. To generate some polynomial it uses finite-field which is Galois field. I am not from mathematical background. Can anybody explain me in simple form to understand this ?
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Galois field is the name that engineers (and especially those studying error correcting codes) use for what mathematicians call finite field. In applications, the most commonly used Galois field is GF$(256)$, also called GF$(2^8)$. Its elements can be thought of as polynomials of degree $7$ or less with binary coefficients ($0$ or $1$). Addition of two field elements is addition of the two polynomials with coefficients being added modulo $2$. Multiplication is polynomial multiplication modulo a polynomial $m(x)$ of degree $8$, that is, multiply the two given polynomials (which may result in a polynomial of degree as much as $14$) and then divide by $m(x)$, throwing away the quotient and keeping only the remainder.
A Galois field is a finite field (from the Wikipedia article):