Subclose Families, Threshold Graphs, and the Weight Hierarchy of Grassmann and Schubert Codes

Details Subclose Families, Threshold Graphs, and the Weight Hierarchy of Grassmann and Schubert Codes Subclose Families, Threshold Graphs, and the Weight Hierarchy of Grassmann and Schubert Codes

2008-04-10

arxiv.org/abs/0804.1669v1

Arithmetic, Geometry, Cryptography and Coding Theory, 87-99, Contemp. Math. 487, Amer. Math. Soc., Providence, RI, 2009.

Mathematics

Combinatorics

11 pages

Scientific paper

We discuss the problem of determining the complete weight hierarchy of linear error correcting codes associated to Grassmann varieties and, more generally, to Schubert varieties in Grassmannians. The problem is partially solved in the case of Grassmann codes, and one of the solutions uses the combinatorial notion of a closed family. We propose a generalization of this to what is called a subclose family. A number of properties of subclose families are proved, and its connection with the notion of threshold graphs and graphs with maximum sum of squares of vertex degrees is outlined.

Affiliated with

Also associated with

No associations

Rating

Subclose Families, Threshold Graphs, and the Weight Hierarchy of Grassmann and Schubert Codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Subclose Families, Threshold Graphs, and the Weight Hierarchy of Grassmann and Schubert Codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Subclose Families, Threshold Graphs, and the Weight Hierarchy of Grassmann and Schubert Codes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-355858