Optimal Binary Linear Codes From Maximal Arcs

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 [2m+s+ 2s- 2m, 2m+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.