Information on Result #691814
Linear OA(1687, 65550, F16, 23) (dual of [65550, 65463, 24]-code), using construction X applied to Ce(22) ⊂ Ce(19) based on
- linear OA(1685, 65536, F16, 23) (dual of [65536, 65451, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(1673, 65536, F16, 20) (dual of [65536, 65463, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-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(8116, 65550, S8, 23) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1687, 49370, F16, 2, 23) (dual of [(49370, 2), 98653, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (64, 87, 49370)-net over F16 | [i] | ||
| 4 | Linear OOA(1687, 32775, F16, 2, 23) (dual of [(32775, 2), 65463, 24]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1687, 5959, F16, 23, 23) (dual of [(5959, 23), 136970, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |