Information on Result #691804
Linear OA(16128, 65551, F16, 34) (dual of [65551, 65423, 35]-code), using construction X applied to Ce(33) ⊂ Ce(29) based on
- linear OA(16125, 65536, F16, 34) (dual of [65536, 65411, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(16113, 65536, F16, 30) (dual of [65536, 65423, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(8171, 65551, S8, 34) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(16128, 51227, F16, 2, 34) (dual of [(51227, 2), 102326, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (94, 128, 51227)-net over F16 | [i] | ||
| 4 | Linear OOA(16128, 32775, F16, 2, 34) (dual of [(32775, 2), 65422, 35]-NRT-code) | [i] | OOA Folding | |