Information on Result #2255113
Linear OA(16123, 65550, F16, 32) (dual of [65550, 65427, 33]-code), using 1 times truncation based on linear OA(16124, 65551, F16, 33) (dual of [65551, 65427, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(28) [i] based on
- linear OA(16121, 65536, F16, 33) (dual of [65536, 65415, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(163, 15, F16, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,16) or 15-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 | OA(8164, 65550, S8, 32) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(16123, 63291, F16, 2, 32) (dual of [(63291, 2), 126459, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (91, 123, 63291)-net over F16 | [i] | ||
| 4 | Linear OOA(16123, 32775, F16, 2, 32) (dual of [(32775, 2), 65427, 33]-NRT-code) | [i] | OOA Folding | |