Information on Result #692051
Linear OA(1647, 4100, F16, 17) (dual of [4100, 4053, 18]-code), using construction X applied to Ce(16) ⊂ Ce(14) based on
- linear OA(1646, 4096, F16, 17) (dual of [4096, 4050, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1643, 4096, F16, 15) (dual of [4096, 4053, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(161, 4, F16, 1) (dual of [4, 3, 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(1646, 4099, F16, 16) (dual of [4099, 4053, 17]-code) | [i] | Truncation | |
| 2 | Linear OOA(1647, 2103, F16, 2, 17) (dual of [(2103, 2), 4159, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (30, 47, 2103)-net over F16 | [i] | ||
| 4 | Linear OOA(1647, 2050, F16, 2, 17) (dual of [(2050, 2), 4053, 18]-NRT-code) | [i] | OOA Folding | |