Optimal Binary Linear Codes from Maximal Arcs

01/04/2020

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by   Ziling Heng, et al.

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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.