Quadratic residue code information

A quadratic residue code is a type of cyclic code. Examples of quadratic residue codes include the ( 7 , 4 ) {\displaystyle (7,4)} Hamming code over G...

In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer...

{\displaystyle l} is a quadratic residue modulo the prime p {\displaystyle p} there is a quadratic residue code which is a cyclic code of length p {\displaystyle...

to construct the extended binary Golay code. Quadratic residue code: Consider the set N of quadratic non-residues (mod 23). This is an 11-element subset...

roots, where φ is the Euler's totient function. Quadratic residue: An integer a is a quadratic residue modulo m, if there exists an integer x such that...

(450) (561) (602) (013). These are the nonzero codewords of the quadratic residue code of length 7 over the Galois field of two elements, GF(2). There...

"block". (We can take any octad of the extended binary Golay code, seen as a quadratic residue code.) From this block, we obtain the other blocks of the S(5...

of the Gleason–Prange theorem on the symmetries of the extended quadratic residue code. Prange was born in Illinois to August Prange and Eugenia Livingston...

distance of at most 2 from exactly one codeword. The code can also be constructed as the quadratic residue code of length 11 over the finite field F3 (i.e., the...

The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field...

Z/23Z ∪ ∞) with entries Χ(m+n) where Χ(∞)=1, Χ(0)=−1, Χ(n)=is the quadratic residue symbol mod 23 for nonzero n. This matrix H is a Paley matrix with...

or may not be a quadratic residue modulo n. This is because for a to be a quadratic residue modulo n, it has to be a quadratic residue modulo every prime...

 is a quadratic residue modulo  L , i ≠ 0 , 0 otherwise {\displaystyle A_{i}={\begin{cases}0&{\mbox{if }}i=0,\\1&{\mbox{if }}i{\mbox{ is a quadratic residue...

if r is a quadratic non-residue modulo p (this is almost the definition of a quadratic non-residue). There are p − 1/2 quadratic non-residues modulo p...

to 3 (mod 4) (this guarantees that each quadratic residue has one square root which is also a quadratic residue), and should be safe primes with a small...

Friedrich Gauss (1777–1855) proved the law of quadratic reciprocity and developed the theory of quadratic forms (in particular, defining their composition)...

English mathematician Raymond Paley. The Paley construction uses quadratic residues in a finite field GF(q) where q is a power of an odd prime number...

scientist Manuel Blum. Given n = p × q a Blum integer, Qn the set of all quadratic residues modulo n and coprime to n and a ∈ Qn. Then: a has four square roots...

Since for these primes p, 2p + 1 is congruent to 7 mod 8, so 2 is a quadratic residue mod 2p + 1, and the multiplicative order of 2 mod 2p + 1 must divide...

ISBN 9780521585330 Russinoff, David M. (1992), "A Mechanical Proof of Quadratic Reciprocity", J. Autom. Reason., 8 (1): 3–21, doi:10.1007/BF00263446,...

contributions to number theory, and developed the theories of binary and ternary quadratic forms. He is considered one of the discoverers of non-Euclidean geometry...

≡ m 2 mod p {\displaystyle c\equiv m^{2}{\bmod {p}}} , so c is a quadratic residue modulo p {\displaystyle p} . Then m p 2 ≡ c 1 2 ( p + 1 ) ≡ c ⋅ c...

method for URAs was modified so that the new arrays were based on quadratic residues rather than pseudo-noise (PN) sequences. Conventional spectral imaging...