Optimal Binary Linear Codes from Maximal Arcs
(2001.01049)Abstract
The binary Hamming codes with parameters $[2m-1, 2m-1-m, 3]$ are perfect. Their extended codes have parameters $[2m, 2m-1-m, 4]$ and are distance-optimal. The first objective of this paper is to construct a class of binary linear codes with parameters $[2{m+s}+2s-2m,2{m+s}+2s-2m-2m-2,4]$, 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 $[2m+2, 2m-2m, 6]$. Both classes of binary linear codes have new parameters.
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