Search results
Results from the WOW.Com Content Network
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [1]
In this case, each symbol can be represented as an -bit value. The sender sends the data points as encoded blocks, and the number of symbols in the encoded block is =. Thus a Reed–Solomon code operating on 8-bit symbols has = = symbols per block
In this case, s is called the least absolute remainder. [3] As with the quotient and remainder, k and s are uniquely determined, except in the case where d = 2n and s = ± n. For this exception, we have: a = k⋅d + n = (k + 1)d − n. A unique remainder can be obtained in this case by some convention—such as always taking the positive value ...
Since the only invertible element is 1, division is the identity function. Elements of GF( p n ) may be represented as polynomials of degree strictly less than n over GF( p ). Operations are then performed modulo m(x) where m(x) is an irreducible polynomial of degree n over GF( p ), for instance using polynomial long division .
Computing the remainder then consists of subtracting multiples of the generator polynomial (). This is just like decimal long division, but even simpler because the only possible multiples at each step are 0 and 1, and the subtractions borrow "from infinity" instead of reducing the upper digits. Because we do not care about the quotient, there ...
The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of ...
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
The long division may begin with a non-zero remainder. The remainder is generally computed using an -bit shift register holding the current remainder, while message bits are added and reduction modulo () is performed. Normal division initializes the shift register to zero, but it may instead be initialized to a non-zero value.