Negacyclic and Cyclic Codes Over
Negacyclic and Cyclic Codes Over
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发表时间：
1999
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通讯作者：
J. Wolfmann
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作者：
J. Wolfmann
的负移定义为使得的置换，长度为的双循环码定义为使得的子集。我们证明了长度为的线性双循环码的Gray像是二元距离不变的（不一定是线性的）循环码。我们还证明了，如果是奇数，那么每个二进制码的格雷图像的线性循环码的长度是等价的（不一定是线性的）循环码，这种等价性明确描述。这最后一个结果解释和推广的存在，已经知道，版本的Kerdock，ESTA，和其他代码作为双扩展循环码。此外，我们还引入了一类二元线性循环码，它们是非线性循环码的Gray象.
The negashift of is defined as the permutation of such that and a negacyclic code of length over is defined as a subset of such that We prove that the Gray image of a linear negacyclic code over of length is a binary distance invariant (not necessary linear) cyclic code. We also prove that, if is odd, then every binary code which is the Gray image of a linear cyclic code over of length is equivalent to a (not necessary linear) cyclic code and this equivalence is explicitely described. This last result explains and generalizes the existence, already known, of versions of Kerdock, Preparata, and others codes as doubly extended cyclic codes. Furthermore, we introduce a family of binary linear cyclic codes which are Gray images of -linear negacyclic codes.