Unlike binary bits of information in ordinary computers, “qubits” consist of quantum particles that have some probability of being in each of two states, designated |0 and |1 , at the same time. When ...

Error-correcting codes defined over finite fields form the cornerstone of reliable digital communication and data storage. Such codes exploit the algebraic structure of finite fields—denoted GF(q)—to ...

The same codes needed to thwart errors in quantum computers may also give the fabric of space-time its intrinsic robustness. Unlike binary bits of information in ordinary computers, “qubits” consist ...

Many types of error-correcting techniques exist, but in data communications, Hamming encoding probably finds the widest use. Unlike serial-port communications that use a single parity bit, Hamming ...