Optimal Binary Linear Codes From Maximal Arcs

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.