Information on Result #691818
Linear OA(1672, 65551, F16, 19) (dual of [65551, 65479, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1657, 65536, F16, 15) (dual of [65536, 65479, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(896, 65551, S8, 19) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1672, 51139, F16, 2, 19) (dual of [(51139, 2), 102206, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (53, 72, 51139)-net over F16 | [i] | ||
| 4 | Linear OOA(1672, 32775, F16, 2, 19) (dual of [(32775, 2), 65478, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1672, 7283, F16, 19, 19) (dual of [(7283, 19), 138305, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |