Information on Result #691803
Linear OA(1663, 65546, F16, 17) (dual of [65546, 65483, 18]-code), using construction X applied to Ce(16) ⊂ Ce(13) based on
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1653, 65536, F16, 14) (dual of [65536, 65483, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(162, 10, F16, 2) (dual of [10, 8, 3]-code or 10-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 | OA(884, 65546, S8, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1663, 40609, F16, 2, 17) (dual of [(40609, 2), 81155, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (46, 63, 40609)-net over F16 | [i] | ||
| 4 | Linear OOA(1663, 32773, F16, 2, 17) (dual of [(32773, 2), 65483, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1663, 8193, F16, 17, 17) (dual of [(8193, 17), 139218, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |