Information on Result #2254844
Linear OA(1647, 4103, F16, 16) (dual of [4103, 4056, 17]-code), using 1 times truncation based on linear OA(1648, 4104, F16, 17) (dual of [4104, 4056, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] 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(1640, 4096, F16, 14) (dual of [4096, 4056, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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 OOA(1647, 3639, F16, 2, 16) (dual of [(3639, 2), 7231, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (31, 47, 3639)-net over F16 | [i] | ||
| 3 | Linear OOA(1647, 2051, F16, 2, 16) (dual of [(2051, 2), 4055, 17]-NRT-code) | [i] | OOA Folding | |