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

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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 )

Date of Publication:

May 2013

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