论文标题
小小的有限字段上最佳LCD代码的几种结构
Several constructions of optimal LCD codes over small finite fields
论文作者
论文摘要
线性互补双重（LCD）代码是线性代码，它们在琐碎的双重代码上与它们相交，由于其在计算复杂性和信息保护方面的实际应用，它们一直很感兴趣并广泛研究。在本文中，我们通过修改一些构造线性代码的典型方法来提供一些通过小有限字段构建LCD代码的方法。我们表明，所有类似奇怪的二进制LCD代码，三元LCD代码和第四纪赫米尔氏菌LCD代码都可以使用修饰方法构建。我们的结果改善了LCD代码最小最小距离的已知下限。此外，我们给出了两个反例，以反驳Bouyuklieva提出的猜想（Des。CodeesCryptogr。89（11）：2445-2461，2021）。
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information protection. In this paper, we give some methods for constructing LCD codes over small finite fields by modifying some typical methods for constructing linear codes. We show that all odd-like binary LCD codes, ternary LCD codes and quaternary Hermitian LCD codes can be constructed using the modified methods. Our results improve the known lower bounds on the largest minimum distances of LCD codes. Furthermore, we give two counterexamples to disprove the conjecture proposed by Bouyuklieva (Des. Codes Cryptogr. 89(11): 2445-2461, 2021).
