有限域上Schubert演算中的子空间码译码问题
Decoding of Subspace Codes, a Problem of Schubert Calculus over Finite Fields
摘要：
舒伯特演算提供了解决枚举问题的代数工具。在系统论、线性代数和物理学中，已有许多应用问题是用Schubert微积分来研究的。当基域是代数闭域时，该方法是最强大的。在这篇文章中，我们首先回顾了一些成功的舒伯特微积分在过去。然后，我们展示了如何使用的子空间码的随机网络编码的解码问题可以制定为舒伯特演算的问题。由于这种应用的基本领域已被假定为一个有限的领域，新的技术将不得不在未来的发展。
英文摘要：
Schubert calculus provides algebraic tools to solve enumerative problems. There have been several applied problems in systems theory, linear algebra and physics which were studied by means of Schubert calculus. The method is most powerful when the base field is algebraically closed. In this article we first review some of the successes Schubert calculus had in the past. Then we show how the problem of decoding of subspace codes used in random network coding can be formulated as a problem in Schubert calculus. Since for this application the base field has to be assumed to be a finite field new techniques will have to be developed in the future.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
