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arXiv · 1806.00448

An Assmus-Mattson Theorem for Rank Metric Codes

Eimear Byrne·Alberto Ravagnani
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Abstract

A $t$-$(n,d,\lambda)$ design over ${\mathbb F}_q$, or a subspace design, is a collection of $d$-dimensional subspaces of ${\mathbb F}_q^n$, called blocks, with the property that every $t$-dimensional subspace of ${\mathbb F}_q^n$ is contained in the same number $\lambda$ of blocks. A collection of matrices in over ${\mathbb F}_q$ is said to hold a subspace design if the set of column spaces of its elements forms the blocks of a subspace design. We use notions of puncturing and shortening of rank metric codes and the rank-metric MacWilliams identities to establish conditions under which the words of a given rank in a linear rank metric code hold a subspace design.

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Eimear Byrne, Alberto Ravagnani. 2018-06-01. An Assmus-Mattson Theorem for Rank Metric Codes. https://arxiv.org/abs/1806.00448

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