By Topic

Toward an explicit construction of nonlinear codes exceeding the Tsfasman-Vladut-Zink bound

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Y. Shany ; Dept. of Electr. Eng.-Syst., Tel Aviv Univ., Ramat-Aviv, Israel

We consider asymptotically good nonlinear codes recently introduced by Xing (2003). The original definition of these codes relies on a nonconstructive averaging argument. In this paper, it is first shown that in some cases, the codes can be constructed without using any averaging arguments. We then introduce an alternative construction of the codes, based on the union of a geometric Goppa code and its cosets. In some cases, the problem of explicitly describing the codes reduces to the problem of explicitly describing certain n elements of the relevant function field, where n is the code length. Moreover, the number of finite-field operations required to construct these n elements after the construction of the generator matrix of the geometric Goppa code is of the order of n3.

Published in:

IEEE Transactions on Information Theory  (Volume:50 ,  Issue: 11 )