On the Message Dimensions of Vector Linearly Solvable Networks

Niladri Das; Brijesh Kumar Rai

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arXiv · 1606.05904

On the Message Dimensions of Vector Linearly Solvable Networks

Niladri Das·Brijesh Kumar Rai

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Abstract

It is known that there exists a network which does not have a scalar linear solution over any finite field but has a vector linear solution when message dimension is $2$ [3]. It is not known whether this result can be generalized for an arbitrary message dimension. In this paper, we show that there exists a network which admits an $m$ dimensional vector linear solution, where $m$ is a positive integer greater than or equal to $2$, but does not have a vector linear solution over any finite field when the message dimension is less than $m$.

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Niladri Das, Brijesh Kumar Rai. 2016-06-19. On the Message Dimensions of Vector Linearly Solvable Networks. https://arxiv.org/abs/1606.05904

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