carryless
Carryless is a term used in mathematics and computer science to describe arithmetic operations that do not involve carries between digit positions. In base-2, carryless addition is the bitwise XOR of corresponding bits, and in many contexts carryless operations model addition and multiplication over the two-element field GF(2) or over polynomial rings GF(2)[x].
Carryless addition: For binary numbers a and b, a ⊕ b is computed by applying XOR to each
Carryless multiplication: Multiplication is performed as polynomial multiplication over GF(2), where binary digits are treated as
Applications: Carryless arithmetic is used in hardware and software implementations of fast polynomial arithmetic, notably via
See also: XOR, GF(2), polynomial arithmetic, CLMUL, CRC, Reed-Solomon.