Inspired by problems in Private Information Retrieval, we consider the setting where two users need to establish a communication protocol to transmit a secret without revealing it to external observers. This is a question of how large a linear code can be, when it is required to agree with a prescribed code on a collection of coordinate sets. We show how the efficiency of such a protocol is determined by the derived matroid of the underlying linear communication code. Furthermore, we provide several sufficient combinatorial conditions for when no secret transmission is possible.

中文翻译：

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使用拟阵理论隐藏信息

受“私人信息检索”中的问题启发，我们考虑了两个用户需要建立通信协议以传输秘密而又不将其透露给外部观察者的设置。这是一个问题，当需要与一组坐标集上的规定代码一致时，线性代码可以有多大。我们展示了如何通过底层线性通信代码的派生类阵确定这种协议的效率。此外，对于无法进行秘密传输的情况，我们提供了几个充分的组合条件。