Information on Result #691807
Linear OA(16115, 65550, F16, 30) (dual of [65550, 65435, 31]-code), using construction X applied to Ce(29) ⊂ Ce(26) based on
- 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(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(8154, 65550, S8, 30) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(16115, 60158, F16, 2, 30) (dual of [(60158, 2), 120201, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (85, 115, 60158)-net over F16 | [i] | ||
| 4 | Linear OOA(16115, 32775, F16, 2, 30) (dual of [(32775, 2), 65435, 31]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(16115, 4370, F16, 30, 30) (dual of [(4370, 30), 130985, 31]-NRT-code) | [i] | OA Folding and Stacking | |