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.

Grotesque

The word grotesque, originally a noun (1560s), from Italian grottesco (through Middle French), literally "of a cave", from Italian grotta (see grotto). The original meaning was restricted to an extravagant style of Ancient Roman decorative art rediscovered and then copied in Rome at the end of the 15th century. The word first was used of paintings found on the walls of basements of Roman ruins that were called at that time Le Grotte (The Grottoes) due to their appearance. These "caves" were in fact rooms and corridors of the Domus Aurea, the unfinished palace complex started by Nero after the Great Fire of Rome in AD 64, which had become overgrown and buried, until they were broken into again, mostly from above. Spreading from Italian to the other European languages, the term was long used largely interchangeably with arabesque and moresque for types of decorative patterns using curving foliage elements.

Since at least the 18th century (in French and German as well as English), grotesque has come to be used as a general adjective for the strange, fantastic, ugly, incongruous, unpleasant, or disgusting, and thus is often used to describe weird shapes and distorted forms such as Halloween masks. In art, performance, and literature, however, grotesque may also refer to something that simultaneously invokes in an audience a feeling of uncomfortable bizarreness as well as sympathetic pity. More specifically, the grotesque forms on Gothic buildings, when not used as drain-spouts, should not be called gargoyles, but rather referred to simply as grotesques, or chimeras.

Grotesque (chess)

In chess, a grotesque is a problem or endgame study which features a particularly unlikely initial position, especially one in which White fights with a very small force against a much larger black army. Grotesques are generally intended to be humorous.

Examples

Ottó Bláthy

A particularly extreme example by Ottó Bláthy is illustrated in the diagram to the left. In the initial position Black has all sixteen pieces remaining and White has just a single pawn on its starting square, yet it is White who will deliver checkmate.

This position in Forsyth-Edwards Notation (FEN) is : 8/8/8/2p5/1pp5/brpp4/qpprpK1P/1nkbn3 w - - 0 1

The solution is:

The fact that the black queen must be on a1 rather than a2 when White plays Nxb3 explains why 2.h4 does not work. Similarly, if the white knight takes a more direct route to the b3 square with 8.Ng6 Qa2 9.Ne5 Qa1 10.Nxc4 Qa2 11.Na5, Black can lose a move with 11...c4! 12.Nxc4 Qa1 13.Na5 Qa2 and there is no mate. This kind of precise timing is quite a common feature in this type of problem.

Grotesque (band)

Grotesque was a Swedish death metal/black metal band formed in Gothenburg, Sweden in September 1988 from the remains of Conquest by Wåhlin (Necrolord) and Nordgren (Virgintaker) with the addition of Lindberg (Goatspell). The band was, however, short-lived and recorded a few demos and an EP. The band's original drummer Shamaatae formed the black metal band Arckanum in 1993. After the demise of Grotesque Lindberg and Svensson started At the Gates, while Necrolord created his own band Liers in Wait and focused more on creating artwork for several bands including Dissection and Emperor. In 1996, three members, Goatspell, Necrolord, and Offensor got back together and recorded two songs for the release of a compilation album, which was later re-released as a split album with At the Gates EP Gardens of Grief.

Grotesque briefly reformed in 2007 for a single invite-only concert on January 26 in Stockholm, to celebrate the publication of Daniel Ekeroth's book Swedish Death Metal. Nirvana 2002 and Interment also reunited for the concert.