By Topic

Asymptotically Good Binary Linear Codes With Asymptotically Good Self-Intersection Spans

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
$31 $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)
Randriambololona, H. ; Telecom ParisTech, Paris, France

If C is a binary linear code, let C〈2〉 be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such that, for C ranging in this family, C〈2〉 also form an asymptotically good family. For this, we use algebraic-geometry codes, concatenation, and a fair amount of bilinear algebra. More precisely, the two main ingredients used in our construction are, first, a description of the symmetric square of an odd degree extension field in terms only of field operations of small degree, and second, a recent result of Garcia-Stichtenoth-Bassa-Beelen on the number of points of curves on such an odd degree extension field.

Published in:

Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 5 )