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.
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entirely replaces the common law in a particular area, leaving the common law inoperative unless and until the code is repealed.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.
Ten-codes, officially known as ten signals, are brevity codes used to represent common phrases in voice communication, particularly by law enforcement and in Citizens Band (CB) radio transmissions.
The codes, developed in 1937 and expanded in 1974 by the Association of Public-Safety Communications Officials-International (APCO), allow for brevity and standardization of message traffic. They have historically been widely used by law enforcement officers in North America but due to the lack of standardization, in 2006 the U.S. federal government recommended they be discontinued in favor of everyday language.
APCO first proposed Morse code brevity codes in the June, 1935 issue of The APCO Bulletin, which were adapted from the procedure symbols of the U.S. Navy.
The development of the APCO Ten Signals began in 1937, when police radio channels were limited to reduce use of speech on the radio. Credit for inventing the codes goes to Charles "Charlie" Hopper, communications director for the Illinois State Police, District 10 in Pesotum, Illinois. Hopper had been involved in radio for years and realized there was a need to abbreviate transmissions on State Police bands. Experienced radio operators knew the first syllable of a transmission was frequently not understood because of quirks in early electronics technology. Radios in the 1930s were based on vacuum tubes powered by a small motor-generator called a dynamotor. The dynamotor took from 1/10 to 1/4 of a second to "spin up" to full power. Police officers were trained to push the microphone button, then pause briefly before speaking; however, sometimes they would forget to wait. Preceding each code with "ten-" gave the radio transmitter time to reach full power. An APCO Bulletin of January 1940 lists codes assigned as part of standardization;
A page is one side of a leaf of paper. It can be used as a measurement of documenting or recording quantity ("that topic covers twelve pages").
Oxford dictionary describes a page as one or both sides of a sheet of paper in a book, magazine, newspaper, or other collection of bound sheets.
In a book, the side of a leaf one rea is called the recto page and the other side is called the verso page. In a spread, one reads the verso page first and then reads the recto page of the next leaf. In English-language books, the recto page is on the right and the verso page is on the left.
The first page of an English-language book is typically a recto page on the right, and the reader flips the pages from right to left. In right-to-left languages (Arabic, Hebrew, and Persian, plus Chinese and Japanese when written vertically), the first page is typically a recto page on the left and the reader flips the pages from left to right.
The process of placing the various text and graphical elements on the page in a visually organized way is called page layout, and the relative lightness or darkness of the page is referred to as its colour.
Pagination is the process of dividing a document into discrete pages, either electronic pages or printed pages. Today printed pages are usually produced by outputting an electronic file to a printing device, such as a desktop printer or a modern printing press. These electronic files may for example be Microsoft Word, PDF or QXD files. They will usually already incorporate the instructions for pagination, among other formatting instructions. Pagination encompasses rules and algorithms for deciding where page breaks will fall, which depend partly on cultural considerations about which content belongs on the same page: for example one may try to avoid widows and orphans. Some systems are more sophisticated than others in this respect. Before the rise of information technology (IT), pagination was a manual process: all pagination was decided by a human. Today, most pagination is performed by machines, although humans often override particular decisions (e.g. by inserting a hard page break).
Page is an occupational surname, derived from page (occupation).