Information on Result #692156
Linear OA(1659, 4112, F16, 20) (dual of [4112, 4053, 21]-code), using construction X applied to Ce(19) ⊂ Ce(14) based on
- linear OA(1655, 4096, F16, 20) (dual of [4096, 4041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
- Reed–Solomon code RS(12,16) [i]
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(1659, 3810, F16, 2, 20) (dual of [(3810, 2), 7561, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (39, 59, 3810)-net over F16 | [i] | ||
| 3 | Linear OOA(1659, 2056, F16, 2, 20) (dual of [(2056, 2), 4053, 21]-NRT-code) | [i] | OOA Folding | |