Quadratic residue code

Quadratic residue codes are a class of error-correcting codes that are derived from the properties of quadratic residues in number theory. These codes are particularly notable in the field of coding theory for their efficiency and ability to detect and correct errors in transmitted data. ### Definition A quadratic residue modulo a prime \( p \) is an integer \( a \) such that there exists some integer \( x \) satisfying the equation \( x^2 \equiv a \mod p \).