Information on Result #616359

Linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20

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(16101, 1048593, F16, 20) (dual of [1048593, 1048492, 21]-code) [i](u, u+v)-Construction
2Linear OA(16102, 1048600, F16, 20) (dual of [1048600, 1048498, 21]-code) [i]
3Linear OA(16103, 1048609, F16, 20) (dual of [1048609, 1048506, 21]-code) [i]
4Linear OA(16104, 1048614, F16, 20) (dual of [1048614, 1048510, 21]-code) [i]
5Linear OA(16105, 1048621, F16, 20) (dual of [1048621, 1048516, 21]-code) [i]
6Linear OA(16106, 1048625, F16, 20) (dual of [1048625, 1048519, 21]-code) [i]
7Linear OA(16107, 1048641, F16, 20) (dual of [1048641, 1048534, 21]-code) [i]
8Linear OA(16108, 1048643, F16, 20) (dual of [1048643, 1048535, 21]-code) [i]
9Linear OA(16108, 1048594, F16, 20) (dual of [1048594, 1048486, 21]-code) [i]Generalized (u, u+v)-Construction
10Linear OOA(1691, 527997, F16, 2, 20) (dual of [(527997, 2), 1055903, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
11Digital (71, 91, 527997)-net over F16 [i]
12Linear OA(16104, 1048590, F16, 20) (dual of [1048590, 1048486, 21]-code) [i](u, u−v, u+v+w)-Construction
13Linear OA(16105, 1048592, F16, 20) (dual of [1048592, 1048487, 21]-code) [i]
14Linear OA(16106, 1048594, F16, 20) (dual of [1048594, 1048488, 21]-code) [i]
15Linear OA(16107, 1048610, F16, 20) (dual of [1048610, 1048503, 21]-code) [i]
16Linear OA(16108, 1048617, F16, 20) (dual of [1048617, 1048509, 21]-code) [i]
17Linear OA(1696, 1048581, F16, 21) (dual of [1048581, 1048485, 22]-code) [i]✔Construction X with Extended Narrow-Sense BCH Codes
18Linear OA(1691, 1048581, F16, 20) (dual of [1048581, 1048490, 21]-code) [i]✔
19Linear OA(16102, 1048587, F16, 22) (dual of [1048587, 1048485, 23]-code) [i]✔
20Linear OA(1692, 1048587, F16, 20) (dual of [1048587, 1048495, 21]-code) [i]✔
21Linear OA(16108, 1048593, F16, 23) (dual of [1048593, 1048485, 24]-code) [i]✔
22Linear OA(1693, 1048593, F16, 20) (dual of [1048593, 1048500, 21]-code) [i]✔
23Linear OA(16115, 1048600, F16, 24) (dual of [1048600, 1048485, 25]-code) [i]✔
24Linear OA(1696, 1048600, F16, 20) (dual of [1048600, 1048504, 21]-code) [i]✔
25Linear OA(1697, 1048602, F16, 20) (dual of [1048602, 1048505, 21]-code) [i]✔
26Linear OA(16122, 1048607, F16, 25) (dual of [1048607, 1048485, 26]-code) [i]✔
27Linear OA(1698, 1048608, F16, 20) (dual of [1048608, 1048510, 21]-code) [i]✔
28Linear OA(16128, 1048613, F16, 26) (dual of [1048613, 1048485, 27]-code) [i]✔
29Linear OA(16100, 1048614, F16, 20) (dual of [1048614, 1048514, 21]-code) [i]✔
30Linear OA(16101, 1048616, F16, 20) (dual of [1048616, 1048515, 21]-code) [i]✔
31Linear OA(16102, 1048622, F16, 20) (dual of [1048622, 1048520, 21]-code) [i]✔
32Linear OA(16104, 1048627, F16, 20) (dual of [1048627, 1048523, 21]-code) [i]✔
33Linear OA(16105, 1048630, F16, 20) (dual of [1048630, 1048525, 21]-code) [i]✔
34Linear OA(16106, 1048636, F16, 20) (dual of [1048636, 1048530, 21]-code) [i]✔
35Linear OA(16104, 1048629, F16, 20) (dual of [1048629, 1048525, 21]-code) [i]✔
36Linear OA(1696, 1048601, F16, 20) (dual of [1048601, 1048505, 21]-code) [i]✔
37Linear OA(16121, 1048602, F16, 25) (dual of [1048602, 1048481, 26]-code) [i]✔Construction XX with a Chain of Extended Narrow-Sense BCH Codes
38Linear OA(16116, 1048602, F16, 24) (dual of [1048602, 1048486, 25]-code) [i]✔