Elias omega coding is a universal code encoding the positive integers. Like Elias gamma coding and Elias delta coding, it works by prefixing the integer with a representation of its order of magnitude in a universal code. Unlike those other two codes, however, Elias omega uses itself recursively to encode that prefix; thus, they are sometimes known as recursive Elias codes. In data compression, a universal code maps the integers (representing messages) onto self-delimiting binary codewords. ... Elias gamma code is a universal code encoding the positive integers. ... Elias delta code is a universal code encoding the positive integers. ... An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ...

To code a number: A number is an abstract entity used originally to describe quantity. ...

1. Put a 'group' of "0" at the end of the representation.
2. If the number to be encoded is 1, stop; if not, add the binary representation of the number as a 'group' to the beginning of the representation.
3. Repeat the previous step, with the number of digits just written, minus 1, as the new number to be encoded.

The code begins: The binary numeral system represents numeric values using two symbols, typically 0 and 1. ...

 1 0 2 10 0 3 11 0 4 10 100 0 5 10 101 0 6 10 110 0 7 10 111 0 8 11 1000 0 9 11 1001 0 10 11 1010 0 11 11 1011 0 12 11 1100 0 13 11 1101 0 14 11 1110 0 15 11 1111 0 16 10 100 10000 0 17 10 100 10001 0 

To decode an Elias omega-coded integer:

1. Start with a variable N, set to a value of 1.
2. Read the first 'group', which will either be a single "0", or a "1" followed by N more digits. If it is a "0", it means the value of the integer is 1; if it starts with a "1", then N becomes the value of the group interpreted as a binary number.
3. Read each successive group; it will either be a single "0", or a "1" followed by N more digits. If it is a "0", it means the value of the integer is N; if it starts with a "1", then N becomes the value of the group interpreted as a binary number.

Omega coding is used in applications where the largest encoded value is not known ahead of time, or to compress data in which small values are much more frequent than large values. In computer science, data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than a more obvious representation would use, through use of specific encoding schemes. ...

See also Elias delta coding, Elias gamma coding Elias delta code is a universal code encoding the positive integers. ... Elias gamma code is a universal code encoding the positive integers. ...