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arXiv · 1511.08889

The joint weight enumerator of an LCD code and its dual

Adel Alahmadi·Michel Deza·Mathieu Dutour Sikirić·Patrick Solé
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Abstract

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.

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Adel Alahmadi, Michel Deza, Mathieu Dutour Sikirić, Patrick Solé. 2015-11-28. The joint weight enumerator of an LCD code and its dual. https://arxiv.org/abs/1511.08889

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