Information on Result #618161

Linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(3278, 1048609, F32, 18) (dual of [1048609, 1048531, 19]-code) [i](u, u+v)-Construction
2Linear OA(3279, 1048620, F32, 18) (dual of [1048620, 1048541, 19]-code) [i]
3Linear OA(3280, 1048622, F32, 18) (dual of [1048622, 1048542, 19]-code) [i]
4Linear OA(3281, 1048640, F32, 18) (dual of [1048640, 1048559, 19]-code) [i]
5Linear OA(3282, 1048642, F32, 18) (dual of [1048642, 1048560, 19]-code) [i]
6Linear OA(3283, 1048652, F32, 18) (dual of [1048652, 1048569, 19]-code) [i]
7Linear OA(3284, 1048670, F32, 18) (dual of [1048670, 1048586, 19]-code) [i]
8Linear OA(3285, 1048675, F32, 18) (dual of [1048675, 1048590, 19]-code) [i]
9Linear OA(3283, 1048653, F32, 18) (dual of [1048653, 1048570, 19]-code) [i]
10Linear OA(3284, 1048592, F32, 18) (dual of [1048592, 1048508, 19]-code) [i]Generalized (u, u+v)-Construction
11Linear OA(3283, 1048591, F32, 18) (dual of [1048591, 1048508, 19]-code) [i]
12Linear OA(3285, 1048594, F32, 18) (dual of [1048594, 1048509, 19]-code) [i]
13Linear OOA(3269, 547090, F32, 2, 18) (dual of [(547090, 2), 1094111, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
14Digital (51, 69, 547090)-net over F32 [i]
15Linear OA(3282, 1048590, F32, 18) (dual of [1048590, 1048508, 19]-code) [i](u, u−v, u+v+w)-Construction
16Linear OA(3283, 1048592, F32, 18) (dual of [1048592, 1048509, 19]-code) [i]
17Linear OA(3284, 1048642, F32, 18) (dual of [1048642, 1048558, 19]-code) [i]
18Linear OA(3285, 1048653, F32, 18) (dual of [1048653, 1048568, 19]-code) [i]
19Linear OA(3273, 1048580, F32, 19) (dual of [1048580, 1048507, 20]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
20Linear OA(3269, 1048580, F32, 18) (dual of [1048580, 1048511, 19]-code) [i]✔
21Linear OA(3278, 1048585, F32, 20) (dual of [1048585, 1048507, 21]-code) [i]✔
22Linear OA(3270, 1048585, F32, 18) (dual of [1048585, 1048515, 19]-code) [i]✔
23Linear OA(3283, 1048590, F32, 21) (dual of [1048590, 1048507, 22]-code) [i]✔
24Linear OA(3271, 1048590, F32, 18) (dual of [1048590, 1048519, 19]-code) [i]✔
25Linear OA(3288, 1048595, F32, 22) (dual of [1048595, 1048507, 23]-code) [i]✔
26Linear OA(3272, 1048595, F32, 18) (dual of [1048595, 1048523, 19]-code) [i]✔
27Linear OA(3293, 1048600, F32, 23) (dual of [1048600, 1048507, 24]-code) [i]✔
28Linear OA(3273, 1048600, F32, 18) (dual of [1048600, 1048527, 19]-code) [i]✔
29Linear OA(3298, 1048605, F32, 24) (dual of [1048605, 1048507, 25]-code) [i]✔
30Linear OA(3274, 1048605, F32, 18) (dual of [1048605, 1048531, 19]-code) [i]✔
31Linear OA(32103, 1048609, F32, 25) (dual of [1048609, 1048506, 26]-code) [i]✔
32Linear OA(32104, 1048611, F32, 25) (dual of [1048611, 1048507, 26]-code) [i]✔
33Linear OA(3275, 1048609, F32, 18) (dual of [1048609, 1048534, 19]-code) [i]✔
34Linear OA(3276, 1048611, F32, 18) (dual of [1048611, 1048535, 19]-code) [i]✔
35Linear OA(32109, 1048616, F32, 26) (dual of [1048616, 1048507, 27]-code) [i]✔
36Linear OA(3277, 1048616, F32, 18) (dual of [1048616, 1048539, 19]-code) [i]✔
37Linear OA(3278, 1048620, F32, 18) (dual of [1048620, 1048542, 19]-code) [i]✔
38Linear OA(3279, 1048622, F32, 18) (dual of [1048622, 1048543, 19]-code) [i]✔
39Linear OOA(3269, 116508, F32, 18, 18) (dual of [(116508, 18), 2097075, 19]-NRT-code) [i]OA Folding and Stacking