Galois geometries and coding theory
Galois geometries and coding theory
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DOI：
10.1007/s10623-015-0156-5
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
T. Etzion;L. Storme
中科院分区：
文献类型：
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作者：
T. Etzion;L. Storme
伽罗瓦几何和编码理论是两个相互影响的研究领域。从早期的例子链接线性MDS码与有限投射空间中的弧，满足Griesmer界限的线性码与minihypers，覆盖半径与饱和集，链接已经发展到函数码，广义投射Reed-Muller码，甚至进一步发展到LDPC码，随机网络码和分布式存储。本文简要回顾了已知的联系，然后重点介绍了新的联系和新的方向。我们提出了新的结果和开放的问题，以刺激伽罗瓦几何，编码理论的研究，并对他们不断发展和增加的相互作用。
Galois geometries and coding theory are two research areas which have been interacting with each other for many decades. From the early examples linking linear MDS codes with arcs in finite projective spaces, linear codes meeting the Griesmer bound with minihypers, covering radius with saturating sets, links have evolved to functional codes, generalized projective Reed–Muller codes, and even further to LDPC codes, random network codes, and distributed storage. This article reviews briefly the known links, and then focuses on new links and new directions. We present new results and open problems to stimulate the research on Galois geometries, coding theory, and on their continuously developing and increasing interactions.