Information on Result #692075
Linear OA(1696, 4104, F16, 34) (dual of [4104, 4008, 35]-code), using construction X applied to Ce(33) ⊂ Ce(30) based on
- linear OA(1694, 4096, F16, 34) (dual of [4096, 4002, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(1688, 4096, F16, 31) (dual of [4096, 4008, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(162, 8, F16, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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(16119, 4169, F16, 34) (dual of [4169, 4050, 35]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(16120, 4171, F16, 34) (dual of [4171, 4051, 35]-code) | [i] | ||
| 3 | Linear OA(16121, 4173, F16, 34) (dual of [4173, 4052, 35]-code) | [i] | ||
| 4 | Linear OOA(1696, 3186, F16, 2, 34) (dual of [(3186, 2), 6276, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (62, 96, 3186)-net over F16 | [i] | ||
| 6 | Linear OOA(1696, 2052, F16, 2, 34) (dual of [(2052, 2), 4008, 35]-NRT-code) | [i] | OOA Folding | |