Xing-Xing Xu

Double circulant LCD codes over $\mathbb{F}_2+u\mathbb{F}_2$ and constructions for binary LCD codes

Linear complementary dual (LCD) codes are linear codes that intersect their dual trivially. We study double circulant (Euclidean) LCD codes over the finite chain ring $R=\mathbb F_2+u\mathbb F_2$, where $u^2=0$. Using the Chinese Remainder Theorem and the factorization of $x^n-1$, we derive an explicit enumeration form...