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The design of codes for distributed storage systems that protects from node failures has been studied for years, and locally repairable code (LRC) is such a method that gives a solution for fast recovery of node failures. Linear complementary dual code (LCD code) is useful for preventing malicious attacks, which helps to secure the system. In this paper, we combine LRC and LCD code by integration of enhancing security and repair efficiency, and propose some techniques for constructing LCD codes with their localities determined. On the basis of these methods and inheriting previous achievements of optimal LCD codes, we give optimal or near-optimal [n, k, d;r] LCD codes for k≤6 and n≥k+1 with relatively small locality, mostly r≤3. Since all of our obtained codes are distance-optimal, in addition, we show that the majority of them are r-optimal and the other 63 codes are all near r-optimal, according to CM bound.
Xubo ZHAO Xiaoping LI Runzhi YANG Qingqing ZHANG Jinpeng LIU
In this paper, we study Hermitian linear complementary dual (abbreviated Hermitian LCD) rank metric codes. A class of Hermitian LCD generalized Gabidulin codes are constructed by qm-self-dual bases of Fq2m over Fq2. Moreover, the exact number of qm-self-dual bases of Fq2m over Fq2 is derived. As a consequence, an upper bound and a lower bound of the number of the constructed Hermitian LCD generalized Gabidulin codes are determined.
We investigate linear complementary dual (LCD) rank-metric codes in this paper. We construct a class of LCD generalized Gabidulin codes by a self-dual basis of an extension field over the base field. Moreover, a class of LCD MRD codes, which are obtained by Cartesian products of a generalized Gabidulin code, is constructed.
Let $mathbb{F}_q$ be a finite field of q elements, $R=mathbb{F}_q+umathbb{F}_q$ (u2=0) and D2n=