Information on Result #691813
Linear OA(1691, 65550, F16, 24) (dual of [65550, 65459, 25]-code), using construction X applied to Ce(23) ⊂ Ce(20) based on
- linear OA(1689, 65536, F16, 24) (dual of [65536, 65447, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(1677, 65536, F16, 21) (dual of [65536, 65459, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(8122, 65550, S8, 24) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1691, 50887, F16, 2, 24) (dual of [(50887, 2), 101683, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (67, 91, 50887)-net over F16 | [i] | ||
| 4 | Linear OOA(1691, 32775, F16, 2, 24) (dual of [(32775, 2), 65459, 25]-NRT-code) | [i] | OOA Folding | |