To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

From Wikipedia, the free encyclopedia

In coding theory, the Lee distance is a distance between two strings and of equal length n over the q-ary alphabet {0, 1, …, q − 1} of size q ≥ 2.

It is a metric, defined as

[1]

Considering the alphabet as the additive group Zq, the Lee distance between two single letters and is the length of shortest path in the Cayley graph (which is circular since the group is cyclic) between them.[2]

If or the Lee distance coincides with the Hamming distance, because both distances are 0 for two single equal symbols and 1 for two single non-equal symbols. For this is not the case anymore, the Lee distance can become bigger than 1.

The metric space induced by the Lee distance is a discrete analog of the elliptic space.[1]

Example

If q = 6, then the Lee distance between 3140 and 2543 is 1 + 2 + 0 + 3 = 6.

History and application

The Lee distance is named after C. Y. Lee. It is applied for phase modulation while the Hamming distance is used in case of orthogonal modulation.

The Berlekamp code is an example of code in the Lee metric.[3] Other significant examples are the Preparata code and Kerdock code; these codes are non-linear when considered over a field, but are linear over a ring.[4]

Also, there exists a Gray isometry (bijection preserving weight) between with the Lee weight and with the Hamming weight.[4]

References

  1. ^ a b Deza, Elena; Deza, Michel (2014), Dictionary of Distances (3rd ed.), Elsevier, p. 52, ISBN 9783662443422
  2. ^ Blahut, Richard E. (2008). Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach. Cambridge University Press. p. 108. ISBN 978-1-139-46946-3.
  3. ^ Roth, Ron (2006). Introduction to Coding Theory. Cambridge University Press. p. 314. ISBN 978-0-521-84504-5.
  4. ^ a b Greferath, Marcus (2009). "An Introduction to Ring-Linear Coding Theory". In Sala, Massimiliano; Mora, Teo; Perret, Ludovic; Sakata, Shojiro; Traverso, Carlo (eds.). Gröbner Bases, Coding, and Cryptography. Springer Science & Business Media. p. 220. ISBN 978-3-540-93806-4.
This page was last edited on 30 January 2021, at 07:50
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.