On the depth spectrum of binary linear codes and their dual
On the depth spectrum of binary linear codes and their dual
复制标题
二进制线性码及其对偶的深度谱
作者：
邓贵新
介绍了有限域上线性码的深度分布和深度谱。得到了码字和码深的许多有趣的性质。本文研究了二元线性码的深度谱与其对偶码之间的两种极端情况。设D(C)为二元线性码C的深度谱，得到D(C)∩D(C⊥)=∅的充分必要条件，以及|D(C)∩D(C⊥)| =⌊n2⌋的充分条件，其中，⌊n2⌋= max{m∈Z: m≤x}。
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) be the depth spectrum of a binary linear code C. We obtain a necessary and sufficient condition that D(C) ∩ D(C⊥) = ∅, and a sufficient condition that |D(C) ∩ D(C⊥)| = ⌊n2⌋, where ⌊n2 ⌋ = max{m ∈ Z : m ≤ x}.