论文标题
二元最佳LCD尺寸的最小距离完全确定
Minimum distances of binary optimal LCD codes of dimension five are completely determined
论文作者
论文摘要
令$ t \ in \ {2,8,10,12,14,16,18 \} $和$ n = 31s+t \ geq 14 $，$ d_ {a}（n，5）$和$ d_ {l}（l}（l}（n，5）$ be barional $ [n，5] $ [n，5] $ courteal lineal cormores and counteal cormores and courteal cormers and countal courte courtecry corment cormers and courtal corment courtecry courte cordare cormeral cormers lc countally dual（lc）我们表明$ [n，5，d_ {a}（n，5）] $最佳线性代码不是LCD代码，那里有一个$ [n，5，d_ {l}（n，5）（n，5）] = [n，5，5，d_ {a}（a a}（n，5）（n，5） $ [n，5，d_ {l}（n，5）] $ optimal lcd代码具有$ d_ {l}（n，5）= 16s+6 = d_ {a}（n，5）-2 $ for $ t = 16 $。结合最佳LCD代码上的已知结果，所有$ [n，5] $ LCD代码的$ d_ {l}（n，5）$已完全确定。
Let $t \in \{2,8,10,12,14,16,18\}$ and $n=31s+t\geq 14$, $d_{a}(n,5)$ and $d_{l}(n,5)$ be distances of binary $[n,5]$ optimal linear codes and optimal linear complementary dual (LCD) codes, respectively. We show that an $[n,5,d_{a}(n,5)]$ optimal linear code is not an LCD code, there is an $[n,5,d_{l}(n,5)]=[n,5,d_{a}(n,5)-1]$ optimal LCD code if $t\neq 16$, and an optimal $[n,5,d_{l}(n,5)]$ optimal LCD code has $d_{l}(n,5)=16s+6=d_{a}(n,5)-2$ for $t=16$. Combined with known results on optimal LCD code, $d_{l}(n,5)$ of all $[n,5]$ LCD codes are completely determined.
