On the depth spectrum of binary linear codes and their dual

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• 作者：Guixin Deng ^{dengguixin@live.com}
• 关键词：Binary code ; Dual code ; Depth distribution ; Depth spectrum
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：340
• 期：4
• 页码：591-595
• 全文大小：407 K
• 卷排序：340

文摘

The depth distribution and depth spectrum of a linear code over finite fields were introduced by Etzion. Many interesting properties of the depth of codewords and codes have been obtained. In this paper we study the two extreme cases between the depth spectrum of binary linear codes and their dual codes. Let D(C)D(C) be the depth spectrum of a binary linear code CC. We obtain a necessary and sufficient condition that D(C)∩D(C⊥)=∅D(C)∩D(C⊥)=∅, and a sufficient condition that |D(C)∩D(C⊥)|=⌊n2⌋, where ⌊n2⌋=max{m∈Z:m≤x}.