BCH code

In coding theory, the BCH codes form a class of cyclic error-correcting codes that are constructed using finite fields. BCH codes were invented in 1959 by French mathematician Alexis Hocquenghem, and independently in 1960 by Raj Bose and D. K. Ray-Chaudhuri. The acronym BCH comprises the initials of these inventors' names.

One of the key features of BCH codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. In particular, it is possible to design binary BCH codes that can correct multiple bit errors. Another advantage of BCH codes is the ease with which they can be decoded, namely, via an algebraic method known as syndrome decoding. This simplifies the design of the decoder for these codes, using small low-power electronic hardware.

BCH codes are used in applications such as satellite communications,compact disc players, DVDs, disk drives, solid-state drives and two-dimensional bar codes.

Definition and illustration

Primitive narrow-sense BCH codes

Hamming space

In statistics and coding theory, a Hamming space is usually the set of all binary strings of length N. It is used in the theory of coding signals and transmission.

More generally, a Hamming space can be defined over any alphabet (set) Q as the set of words of a fixed length N with letters from Q. If Q is a finite field, then a Hamming space over Q is an N-dimensional vector space over Q. In the typical, binary case, the field is thus GF(2) (also denoted by Z₂).

In coding theory, if Q has q elements, then any subset C (usually assumed of cardinality at least two) of the N-dimensional Hamming space over Q is called a q-ary code of length N; the elements of C are called codewords. In the case where C is a linear subspace of its Hamming space, it is called a linear code. A typical example of linear code is the Hamming code. Codes defined via a Hamming space necessarily have the same length for every codeword, so they are called block codes when it is necessary to distinguish them from variable-length codes that are defined by unique factorization on a monoid.

Code (album)

Code (stylized as C O D E) is an album by British electronic band Cabaret Voltaire. The track "Don't Argue" was released as a single, as was "Here To Go".

The lyrics (and title) of "Don't Argue" incorporate verbatim a number of sentences from the narration of the 1945 short film Your Job in Germany, directed by Frank Capra. The film was aimed at American soldiers occupying Germany and strongly warned against trusting or fraternizing with German citizens.

Track listing

Personnel

Code (law)

A code is a type of legislation that purports to exhaustively cover a complete system of laws or a particular area of law as it existed at the time the code was enacted, by a process of codification. Though the process and motivations for codification are similar in different common law and civil law systems, their usage is different. In a civil law country, a Code typically exhaustively covers the complete system of law, such as civil law or criminal law. By contrast, in a common law country with legislative practices in the English tradition, a Code is a less common form of legislation, which differs from usual legislation that, when enacted, modify the existing common law only to the extent of its express or implicit provision, but otherwise leaves the common law intact. By contrast, a code entirely replaces the common law in a particular area, leaving the common law inoperative unless and until the code is repealed. In a third case of slightly different usage, in the United States and other common law countries that have adopted similar legislative practices, a Code is a standing body of statute law on a particular area, which is added to, subtracted from, or otherwise modified by individual legislative enactments.

BCH

BCH and BCh may refer to: