Skip to main content

linear codes

linear codes In coding theory, codes whose encoding and decoding operations may be expressed in terms of linear operations. The term is usually applied to certain error-correcting codes in which the encoding operation involves a generator matrix and the decoding operation involves a parity-check matrix. Linear codes are, therefore, also called parity-check codes. A particular linear code forms a commutative group that has the zero codeword as its identity.

In the case of linear (n, k) block codes, the generator matrix is k × n and the parity-check matrix is (n k) × n; the elements of both matrices are elements of the base field (this being error-correcting codes for binary codes). See also convolutional code.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"linear codes." A Dictionary of Computing. . Encyclopedia.com. 11 Dec. 2018 <https://www.encyclopedia.com>.

"linear codes." A Dictionary of Computing. . Encyclopedia.com. (December 11, 2018). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/linear-codes

"linear codes." A Dictionary of Computing. . Retrieved December 11, 2018 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/linear-codes

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.