Information on Result #692055
Linear OA(1637, 4096, F16, 13) (dual of [4096, 4059, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13
Mode: Constructive and linear.
This result is hidden, because other results with identical parameters exist.
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 OOA(1637, 2850, F16, 2, 13) (dual of [(2850, 2), 5663, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (24, 37, 2850)-net over F16 | [i] | ||
| 3 | Linear OA(1640, 4099, F16, 14) (dual of [4099, 4059, 15]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 4 | Linear OA(1637, 4099, F16, 13) (dual of [4099, 4062, 14]-code) | [i] | ✔ | |
| 5 | Linear OA(1649, 4108, F16, 17) (dual of [4108, 4059, 18]-code) | [i] | ✔ | |
| 6 | Linear OA(1639, 4107, F16, 13) (dual of [4107, 4068, 14]-code) | [i] | ✔ | |
| 7 | Linear OA(1653, 4112, F16, 18) (dual of [4112, 4059, 19]-code) | [i] | ✔ | |
| 8 | Linear OA(1658, 4117, F16, 19) (dual of [4117, 4059, 20]-code) | [i] | ✔ | |
| 9 | Linear OA(1642, 4116, F16, 13) (dual of [4116, 4074, 14]-code) | [i] | ✔ | |
| 10 | Linear OA(1662, 4120, F16, 20) (dual of [4120, 4058, 21]-code) | [i] | ✔ | |
| 11 | Linear OA(1663, 4122, F16, 20) (dual of [4122, 4059, 21]-code) | [i] | ✔ | |
| 12 | Linear OA(1667, 4126, F16, 21) (dual of [4126, 4059, 22]-code) | [i] | ✔ | |
| 13 | Linear OA(1671, 4129, F16, 22) (dual of [4129, 4058, 23]-code) | [i] | ✔ | |
| 14 | Linear OA(1672, 4131, F16, 22) (dual of [4131, 4059, 23]-code) | [i] | ✔ | |
| 15 | Linear OA(1676, 4134, F16, 23) (dual of [4134, 4058, 24]-code) | [i] | ✔ | |
| 16 | Linear OA(1677, 4136, F16, 23) (dual of [4136, 4059, 24]-code) | [i] | ✔ | |
| 17 | Linear OA(1681, 4140, F16, 24) (dual of [4140, 4059, 25]-code) | [i] | ✔ | |
| 18 | Linear OA(1686, 4145, F16, 25) (dual of [4145, 4059, 26]-code) | [i] | ✔ | |
| 19 | Linear OA(1691, 4150, F16, 26) (dual of [4150, 4059, 27]-code) | [i] | ✔ | |
| 20 | Linear OA(1657, 4114, F16, 19) (dual of [4114, 4057, 20]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 21 | Linear OA(1654, 4114, F16, 18) (dual of [4114, 4060, 19]-code) | [i] | ✔ | |