Information on Result #2286747
Linear OA(16103, 4108, F16, 36) (dual of [4108, 4005, 37]-code), using 1 times code embedding in larger space based on linear OA(16102, 4107, F16, 36) (dual of [4107, 4005, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(32) [i] based on
- linear OA(16100, 4096, F16, 36) (dual of [4096, 3996, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(1691, 4096, F16, 33) (dual of [4096, 4005, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(162, 11, F16, 2) (dual of [11, 9, 3]-code or 11-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 | Linear OOA(16103, 3678, F16, 2, 36) (dual of [(3678, 2), 7253, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (67, 103, 3678)-net over F16 | [i] | ||
| 3 | Linear OOA(16103, 2054, F16, 2, 36) (dual of [(2054, 2), 4005, 37]-NRT-code) | [i] | OOA Folding | |