Information on Result #616350

Linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19

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(1695, 1048593, F16, 19) (dual of [1048593, 1048498, 20]-code) [i](u, u+v)-Construction
2Linear OA(1696, 1048600, F16, 19) (dual of [1048600, 1048504, 20]-code) [i]
3Linear OA(1697, 1048609, F16, 19) (dual of [1048609, 1048512, 20]-code) [i]
4Linear OA(1698, 1048614, F16, 19) (dual of [1048614, 1048516, 20]-code) [i]
5Linear OA(1699, 1048621, F16, 19) (dual of [1048621, 1048522, 20]-code) [i]
6Linear OA(16100, 1048625, F16, 19) (dual of [1048625, 1048525, 20]-code) [i]
7Linear OA(16101, 1048641, F16, 19) (dual of [1048641, 1048540, 20]-code) [i]
8Linear OA(16102, 1048661, F16, 19) (dual of [1048661, 1048559, 20]-code) [i]
9Linear OA(16101, 1048592, F16, 19) (dual of [1048592, 1048491, 20]-code) [i]Generalized (u, u+v)-Construction
10Linear OA(16100, 1048591, F16, 19) (dual of [1048591, 1048491, 20]-code) [i]
11Linear OA(16102, 1048594, F16, 19) (dual of [1048594, 1048492, 20]-code) [i]
12Linear OA(1699, 1048590, F16, 19) (dual of [1048590, 1048491, 20]-code) [i](u, u−v, u+v+w)-Construction
13Linear OA(16100, 1048592, F16, 19) (dual of [1048592, 1048492, 20]-code) [i]
14Linear OA(16101, 1048610, F16, 19) (dual of [1048610, 1048509, 20]-code) [i]
15Linear OA(16102, 1048617, F16, 19) (dual of [1048617, 1048515, 20]-code) [i]
16Linear OA(1691, 1048581, F16, 20) (dual of [1048581, 1048490, 21]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
17Linear OA(1686, 1048581, F16, 19) (dual of [1048581, 1048495, 20]-code) [i]✔
18Linear OA(1697, 1048587, F16, 21) (dual of [1048587, 1048490, 22]-code) [i]✔
19Linear OA(1687, 1048587, F16, 19) (dual of [1048587, 1048500, 20]-code) [i]✔
20Linear OA(16103, 1048593, F16, 22) (dual of [1048593, 1048490, 23]-code) [i]✔
21Linear OA(1689, 1048594, F16, 19) (dual of [1048594, 1048505, 20]-code) [i]✔
22Linear OA(16110, 1048600, F16, 23) (dual of [1048600, 1048490, 24]-code) [i]✔
23Linear OA(1691, 1048600, F16, 19) (dual of [1048600, 1048509, 20]-code) [i]✔
24Linear OA(1692, 1048602, F16, 19) (dual of [1048602, 1048510, 20]-code) [i]✔
25Linear OA(16117, 1048607, F16, 24) (dual of [1048607, 1048490, 25]-code) [i]✔
26Linear OA(1693, 1048608, F16, 19) (dual of [1048608, 1048515, 20]-code) [i]✔
27Linear OA(16123, 1048613, F16, 25) (dual of [1048613, 1048490, 26]-code) [i]✔
28Linear OA(1695, 1048614, F16, 19) (dual of [1048614, 1048519, 20]-code) [i]✔
29Linear OA(1696, 1048616, F16, 19) (dual of [1048616, 1048520, 20]-code) [i]✔
30Linear OA(1697, 1048622, F16, 19) (dual of [1048622, 1048525, 20]-code) [i]✔
31Linear OA(1699, 1048627, F16, 19) (dual of [1048627, 1048528, 20]-code) [i]✔
32Linear OA(16100, 1048630, F16, 19) (dual of [1048630, 1048530, 20]-code) [i]✔
33Linear OA(1699, 1048629, F16, 19) (dual of [1048629, 1048530, 20]-code) [i]✔
34Linear OA(1691, 1048601, F16, 19) (dual of [1048601, 1048510, 20]-code) [i]✔
35Linear OA(16116, 1048602, F16, 24) (dual of [1048602, 1048486, 25]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
36Linear OA(16111, 1048602, F16, 23) (dual of [1048602, 1048491, 24]-code) [i]✔
37Linear OOA(1686, 116508, F16, 19, 19) (dual of [(116508, 19), 2213566, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row