` Higher Weights of Affine Grassmann Codes and Their Duals

Higher Weights of Affine Grassmann Codes and Their Duals


Mrinmoy Datta

Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India

E-Mail: mrinmoy.dat@gmail.com

Sudhir R. Ghorpade

Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India

E-Mail: srg@math.iitb.ac.in


Abstract: We consider the question of determining the higher weights or the generalized Hamming weights of affine Grassmann codes and their duals. Several initial as well as terminal higher weights of affine Grassmann codes of an arbitrary level are determined explicitly. In the case of duals of these codes, we give a formula for many initial as well as terminal higher weights. As a special case, we obtain an alternative simpler proof of the formula of Beelen et al for the minimum distance of the dual of an affine Grasmann code.


1 Introduction 1
2 Initial Higher Weights 3
3 Terminal Higher Weights 7
4 Higher Weights of Duals of Affine Grassmann Codes 8
Appendix: A Geometric Approach to Higher Weights 10
References 13


This paper is published in: Algorithmic Arithmetic, Geometry, and Coding Theory (Luminy, France, June 2013), S. Ballet, M. Perret, and A. Zaytsev Eds., Contemporary Mathematics, Vol. 637, American Mathematical Society, Providence, RI, 2015, pp. 79-91.

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