Subspace Polynomials and Cyclic Subspace Codes
Subspace Polynomials and Cyclic Subspace Codes
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DOI：
10.1109/tit.2016.2520479
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发表时间：
2016-03
影响因子：
2.5
通讯作者：
Eli Ben-Sasson;T. Etzion;Ariel Gabizon;Netanel Raviv
中科院分区：
文献类型：
--
作者：
Eli Ben-Sasson;T. Etzion;Ariel Gabizon;Netanel Raviv
近年来，子空间码由于在随机网络编码纠错中的应用而受到越来越多的关注。特别地，循环子空间码是具有高效编码和解码算法的大型码的可能候选者。在本文中，我们考虑这样的循环码，并提供最佳的代码，其码字没有完整的轨道的建设。我们进一步介绍了一种新的方法来表示子空间码的一类多项式称为子空间多项式。我们提出了这样的码的一些结构，这是循环的，并分析其参数。
Subspace codes have received an increasing interest recently due to their application in error correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and decoding algorithms. In this paper, we consider such cyclic codes and provide constructions of optimal codes for which their codewords do not have full orbits. We further introduce a new way to represent subspace codes by a class of polynomials called subspace polynomials. We present some constructions of such codes, which are cyclic and analyze their parameters.