ECC dictionary Q

quadratic residue codes:

Let m > 2 be a prime number. The integers 1 ≤ a ≤ m-1 for which a ≡ x² (mod m), for some x in ZZ, are called quadratic residues mod m. The remaining elements of {1, 2, ..., m-1} are called quadratic non-residues mod m. Let n be a positive integer relatively prime to q and let alpha be a primitive n-th root of unity. Let p and n be distinct primes and assume that p is a quadratic residue (mod n). The quadratic residue code of length n over GF(p) is the cyclic code whose generator polynomial has zeros { α^k | k is a square (mod n) }.