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The smallest length of eight-dimensional binary linear codes with prescribed minimum distance

机译:具有规定最小距离的八维二进制线性代码的最小长度

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摘要

Let n(8,d) be the smallest integer n for which a binary linear code of length n, dimension 8, and minimum distance d exists. We prove that n(8,18)=42, n(8,26)=58, n(8,28)=61, n(8,30)=65, n(8,34)=74, n(8,36)=77, n(8,38)=81, n(8,42)=89, and n(8,60)=124. After these results, all values of n(8,d) are known.
机译:令n(8,d)为最小整数n,对于该整数,存在长度为n,尺寸为8,最小距离为d的二进制线性代码。我们证明n(8,18)= 42,n(8,26)= 58,n(8,28)= 61,n(8,30)= 65,n(8,34)= 74,n( 8,36)= 77,n(8,38)= 81,n(8,42)= 89,n(8,60)= 124。在这些结果之后,n(8,d)的所有值都是已知的。

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