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Standard Book Number (ISBN) uses modulo 11 (for 10-digit ISBN) or modulo 10 (for 13-digit ISBN) arithmetic for error detection. Likewise, International...

result are stored; the result is said to wrap around the maximum (i.e. modulo a power of the radix, usually two in modern computers, but sometimes ten...

linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By...

In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable...

sum) modulo 10. This would catch any single-digit error, as such an error would always change the sum, but does not catch any transposition errors (switching...

(11 minus the remainder of the sum of the products modulo 11) modulo 11. Taking the remainder modulo 11 a second time accounts for the possibility that...

size (modulo 128 and modulo 32768) where the maximum number of outstanding frames for acknowledgment is raised from 7 (modulo 8) to 127 (modulo 128) and...

cost of eliminating "modulo bias" when generating random integers for a Fisher-Yates shuffle depends on the approach (classic modulo, floating-point multiplication...

all memory registers start with a value of 0. The encoder has n modulo-2 adders (a modulo 2 adder can be implemented with a single Boolean XOR gate, where...

indicates whether an error has occurred, and if so, for which codeword bit. Performing this multiplication (again, entries modulo 2): z = H r = ( 1 0 1...

division in the ring of polynomials over GF(2) (the finite field of integers modulo 2). That is, the set of polynomials where each coefficient is either zero...

prime field of order p {\displaystyle p} may be constructed as the integers modulo p {\displaystyle p} , Z / p Z {\displaystyle \mathbb {Z} /p\mathbb {Z} }...

with errors key exchange by Peikert. Denote by T = R / Z {\displaystyle \mathbb {T} =\mathbb {R} /\mathbb {Z} } the additive group on reals modulo one...

A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital...

the polynomial "left over" after dividing one polynomial by another. The modulo operation is the operation that produces such a remainder when given a dividend...

+ r0 is any nonzero polynomial modulo 2 with at most t nonzero coefficients, then R(x) is not a multiple of P(x) modulo 2. If follows that the corresponding...

a prime, then the only square roots of 1 modulo n are 1 and −1. Proof Certainly 1 and −1, when squared modulo n, always yield 1. It remains to show that...

(that is, any result congruent to 8 modulo 9). In particular, casting out nines does not catch transposition errors, such as 1324 instead of 1234. In other...

the remainder operator (modulo), and in Java, if its first operand is negative, the result can also be negative (unlike the modulo used in mathematics)....

argument (product in the above example) to the function. Tail recursion modulo cons is a generalization of tail-recursion optimization introduced by David...