Information on Result #2255079
Linear OA(1693, 4107, F16, 32) (dual of [4107, 4014, 33]-code), using 1 times truncation based on linear OA(1694, 4108, F16, 33) (dual of [4108, 4014, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
- linear OA(1691, 4096, F16, 33) (dual of [4096, 4005, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(1682, 4096, F16, 29) (dual of [4096, 4014, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(163, 12, F16, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,16) or 12-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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(1693, 3941, F16, 2, 32) (dual of [(3941, 2), 7789, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (61, 93, 3941)-net over F16 | [i] | ||
| 3 | Linear OOA(1693, 2053, F16, 2, 32) (dual of [(2053, 2), 4013, 33]-NRT-code) | [i] | OOA Folding | |