Information on Result #692068
Linear OA(1610, 4099, F16, 4) (dual of [4099, 4089, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(1610, 4096, F16, 4) (dual of [4096, 4086, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(167, 4096, F16, 3) (dual of [4096, 4089, 4]-code or 4096-cap in PG(6,16)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-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 OOA(1610, 4099, F16, 2, 4) (dual of [(4099, 2), 8188, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (6, 10, 4099)-net over F16 | [i] | ||
| 3 | Linear OOA(1610, 2049, F16, 2, 4) (dual of [(2049, 2), 4088, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(1610, 2049, F16, 4, 4) (dual of [(2049, 4), 8186, 5]-NRT-code) | [i] | OA Folding and Stacking | |