Information on Result #692078
Linear OA(1686, 4103, F16, 30) (dual of [4103, 4017, 31]-code), using construction X applied to Ce(29) ⊂ Ce(27) based on
- linear OA(1685, 4096, F16, 30) (dual of [4096, 4011, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(1679, 4096, F16, 28) (dual of [4096, 4017, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(161, 7, F16, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(16107, 4168, F16, 30) (dual of [4168, 4061, 31]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(16108, 4170, F16, 30) (dual of [4170, 4062, 31]-code) | [i] | ||
| 3 | Linear OA(16109, 4172, F16, 30) (dual of [4172, 4063, 31]-code) | [i] | ||
| 4 | Linear OOA(1686, 3392, F16, 2, 30) (dual of [(3392, 2), 6698, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (56, 86, 3392)-net over F16 | [i] | ||
| 6 | Linear OOA(1686, 2051, F16, 2, 30) (dual of [(2051, 2), 4016, 31]-NRT-code) | [i] | OOA Folding | |