2015/11/28 by Adel Alahmadi, Michel Deza, Alahmadi, Adel +5
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Metric Geometry (math.MG) #cs.IT #math.IT #math.MG
paper · pdf · doi:10.48550/arxiv.1511.08889
5 pages, 3 tables
arxiv created 2015/11/28 · arxiv updated 2015/12/01
A binary linear code is called \em LCD if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on the size of an LCD code of given length and minimum distance. In addition, we show that this polynomial is, in general, an invariant of a matrix group of dimension 4 and order 12. Also, we sketch a Gleason formula for this weight enumerator.