论文标题
最佳二进制线性代码来自最大弧
Optimal Binary Linear Codes from Maximal Arcs
论文作者
论文摘要
具有参数的二进制锤码$ [2^m-1，2^m-1-m，3] $是完美的。他们的扩展代码具有参数$ [2^m，2^m-1-m，4] $，并且是距离最佳的。本文的第一个目的是构建一类带有参数的二进制线性代码$ [2^{M+S}+2^s-2^m，2^{M+S}+2^S-2^S-2^S-2^M-2M-2,4] $，它们的信息速率比扩展的二进制锤击代码更好，并且也是距离距离远程 - 距离。第二个目标是构建一类具有参数的距离最佳二进制代码$ [2^m+2，2^m-2m，6] $。两类二进制线性代码都有新的参数。
The binary Hamming codes with parameters $[2^m-1, 2^m-1-m, 3]$ are perfect. Their extended codes have parameters $[2^m, 2^m-1-m, 4]$ and are distance-optimal. The first objective of this paper is to construct a class of binary linear codes with parameters $[2^{m+s}+2^s-2^m,2^{m+s}+2^s-2^m-2m-2,4]$, which have better information rates than the class of extended binary Hamming codes, and are also distance-optimal. The second objective is to construct a class of distance-optimal binary codes with parameters $[2^m+2, 2^m-2m, 6]$. Both classes of binary linear codes have new parameters.
