Information on Result #616343
Linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, 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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(1690, 1048593, F16, 18) (dual of [1048593, 1048503, 19]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(1691, 1048600, F16, 18) (dual of [1048600, 1048509, 19]-code) | [i] | ||
| 3 | Linear OA(1692, 1048609, F16, 18) (dual of [1048609, 1048517, 19]-code) | [i] | ||
| 4 | Linear OA(1693, 1048614, F16, 18) (dual of [1048614, 1048521, 19]-code) | [i] | ||
| 5 | Linear OA(1694, 1048621, F16, 18) (dual of [1048621, 1048527, 19]-code) | [i] | ||
| 6 | Linear OA(1695, 1048625, F16, 18) (dual of [1048625, 1048530, 19]-code) | [i] | ||
| 7 | Linear OA(1696, 1048641, F16, 18) (dual of [1048641, 1048545, 19]-code) | [i] | ||
| 8 | Linear OA(1696, 1048592, F16, 18) (dual of [1048592, 1048496, 19]-code) | [i] | Generalized (u, u+v)-Construction | |
| 9 | Linear OA(1695, 1048591, F16, 18) (dual of [1048591, 1048496, 19]-code) | [i] | ||
| 10 | Linear OA(1694, 1048590, F16, 18) (dual of [1048590, 1048496, 19]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 11 | Linear OA(1695, 1048592, F16, 18) (dual of [1048592, 1048497, 19]-code) | [i] | ||
| 12 | Linear OA(1696, 1048610, F16, 18) (dual of [1048610, 1048514, 19]-code) | [i] | ||
| 13 | Linear OA(1686, 1048581, F16, 19) (dual of [1048581, 1048495, 20]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 14 | Linear OA(1681, 1048581, F16, 18) (dual of [1048581, 1048500, 19]-code) | [i] | ✔ | |
| 15 | Linear OA(1692, 1048587, F16, 20) (dual of [1048587, 1048495, 21]-code) | [i] | ✔ | |
| 16 | Linear OA(1683, 1048588, F16, 18) (dual of [1048588, 1048505, 19]-code) | [i] | ✔ | |
| 17 | Linear OA(1698, 1048593, F16, 21) (dual of [1048593, 1048495, 22]-code) | [i] | ✔ | |
| 18 | Linear OA(1684, 1048594, F16, 18) (dual of [1048594, 1048510, 19]-code) | [i] | ✔ | |
| 19 | Linear OA(16105, 1048600, F16, 22) (dual of [1048600, 1048495, 23]-code) | [i] | ✔ | |
| 20 | Linear OA(1686, 1048600, F16, 18) (dual of [1048600, 1048514, 19]-code) | [i] | ✔ | |
| 21 | Linear OA(1687, 1048602, F16, 18) (dual of [1048602, 1048515, 19]-code) | [i] | ✔ | |
| 22 | Linear OA(16112, 1048607, F16, 23) (dual of [1048607, 1048495, 24]-code) | [i] | ✔ | |
| 23 | Linear OA(1688, 1048608, F16, 18) (dual of [1048608, 1048520, 19]-code) | [i] | ✔ | |
| 24 | Linear OA(16118, 1048613, F16, 24) (dual of [1048613, 1048495, 25]-code) | [i] | ✔ | |
| 25 | Linear OA(1690, 1048614, F16, 18) (dual of [1048614, 1048524, 19]-code) | [i] | ✔ | |
| 26 | Linear OA(1691, 1048616, F16, 18) (dual of [1048616, 1048525, 19]-code) | [i] | ✔ | |
| 27 | Linear OA(16126, 1048621, F16, 25) (dual of [1048621, 1048495, 26]-code) | [i] | ✔ | |
| 28 | Linear OA(1692, 1048622, F16, 18) (dual of [1048622, 1048530, 19]-code) | [i] | ✔ | |
| 29 | Linear OA(1694, 1048627, F16, 18) (dual of [1048627, 1048533, 19]-code) | [i] | ✔ | |
| 30 | Linear OA(1695, 1048630, F16, 18) (dual of [1048630, 1048535, 19]-code) | [i] | ✔ | |
| 31 | Linear OA(1694, 1048629, F16, 18) (dual of [1048629, 1048535, 19]-code) | [i] | ✔ | |
| 32 | Linear OA(1686, 1048601, F16, 18) (dual of [1048601, 1048515, 19]-code) | [i] | ✔ | |
| 33 | Linear OA(16111, 1048602, F16, 23) (dual of [1048602, 1048491, 24]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 34 | Linear OA(16106, 1048602, F16, 22) (dual of [1048602, 1048496, 23]-code) | [i] | ✔ | |
| 35 | Linear OA(1682, 1048593, F16, 16) (dual of [1048593, 1048511, 17]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |