Information on Result #692111
Linear OA(1690, 4107, F16, 31) (dual of [4107, 4017, 32]-code), using construction X applied to Ce(30) ⊂ Ce(27) based on
- 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(1679, 4096, F16, 28) (dual of [4096, 4017, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(162, 11, F16, 2) (dual of [11, 9, 3]-code or 11-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(16111, 4172, F16, 31) (dual of [4172, 4061, 32]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(16112, 4174, F16, 31) (dual of [4174, 4062, 32]-code) | [i] | ||
| 3 | Linear OA(16113, 4176, F16, 31) (dual of [4176, 4063, 32]-code) | [i] | ||
| 4 | Linear OOA(1690, 3843, F16, 2, 31) (dual of [(3843, 2), 7596, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (59, 90, 3843)-net over F16 | [i] | ||
| 6 | Linear OOA(1690, 2053, F16, 2, 31) (dual of [(2053, 2), 4016, 32]-NRT-code) | [i] | OOA Folding | |