Singleton boundIn coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It is also known as the Joshibound. proved by and even earlier by . The minimum distance of a set of codewords of length is defined as where is the Hamming distance between and . The expression represents the maximum number of possible codewords in a -ary block code of length and minimum distance .
Error correction codeIn computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.
Johnson boundIn applied mathematics, the Johnson bound (named after Selmer Martin Johnson) is a limit on the size of error-correcting codes, as used in coding theory for data transmission or communications. Let be a q-ary code of length , i.e. a subset of . Let be the minimum distance of , i.e. where is the Hamming distance between and . Let be the set of all q-ary codes with length and minimum distance and let denote the set of codes in such that every element has exactly nonzero entries. Denote by the number of elements in .
Block codeIn coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of all block codes in a unified way.
