Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to its wide applications. In this paper, we give some methods for constructing LCD codes over small fields by modifying some known methods. We show that all odd-like binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes can be constructed by the modified methods. Using these methods, we construct a lot of optimal binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes, which improve the known lower bounds on the largest minimum weights. Furthermore, we give two counterexamples to show that the conjecture proposed by Bouyuklieva (Des. Codes Cryptogr. 89(11): 2445-2461, 2021) is invalid.
翻译：线性互补双轨(LCD)代码是线性代码,它们互不相干,由于其广泛应用而引起人们的兴趣并进行了广泛研究。在本文中,我们通过修改一些已知方法,为在小领域建立LCD代码提供了一些方法。我们表明,所有奇异的二进式LCD代码、双进式LCD代码和四进式Hermitian LCD代码都可以用修改的方法构建。我们使用这些方法,构建了许多最佳的二进式LCD代码、双进式LCD代码和四进式Hermitian LCD代码,这些代码改进了已知的最大最小重量的较低界限。此外,我们给出了两个反示例,以表明布尤克利耶娃瓦(Des. Cryptogr. 89(11) : 2445-2461, 2021) 提出的假设无效。
相关内容
微信扫码咨询专知VIP会员