The joint weight enumerator of an LCD code and its dual
Copyright policy )The joint weight enumerator of an LCD code and its dual
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.
5 pages, 3 tables
- King Abdulaziz University Saudi Arabia
- Hospital de Clínicas da Unicamp Brazil
- Ruđer Bošković Institute Croatia
- Télécom ParisTech France
- Laboratoire Traitement et Communication de l’Information France
FOS: Computer and information sciences, linear programming bounds, linear binary code, Computer Science - Information Theory, Information Theory (cs.IT), Metric Geometry (math.MG), LCD code, Mathematics - Metric Geometry, Linear programming, FOS: Mathematics, Linear binary code ; LCD code ; Linear programming bounds, Linear codes (general theory)
FOS: Computer and information sciences, linear programming bounds, linear binary code, Computer Science - Information Theory, Information Theory (cs.IT), Metric Geometry (math.MG), LCD code, Mathematics - Metric Geometry, Linear programming, FOS: Mathematics, Linear binary code ; LCD code ; Linear programming bounds, Linear codes (general theory)
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