2000 character limit reached
On the minimum weights of binary LCD codes and ternary LCD codes
Published 23 Aug 2019 in cs.IT, math.CO, and math.IT | (1908.08661v3)
Abstract: Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight $d_2(n,k)$ among all binary LCD $[n,k]$ codes and the largest minimum weight $d_3(n,k)$ among all ternary LCD $[n,k]$ codes. The largest minimum weights $d_2(n,5)$ and $d_3(n,4)$ are partially determined. We also determine the largest minimum weights $d_2(n,n-5)$, $d_3(n,n-i)$ for $i \in {2,3,4}$, and $d_3(n,k)$ for $n \in {11,12,\ldots,19}$.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
