Information on Result #1051305
Linear OOA(284, 16389, F2, 4, 11) (dual of [(16389, 4), 65472, 12]-NRT-code), using OOA 4-folding based on linear OA(284, 65556, F2, 11) (dual of [65556, 65472, 12]-code), using
- 2 times code embedding in larger space [i] based on linear OA(282, 65554, F2, 11) (dual of [65554, 65472, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(281, 65536, F2, 11) (dual of [65536, 65455, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(265, 65536, F2, 9) (dual of [65536, 65471, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
- dual of repetition code with length 18 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
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(285, 16389, F2, 4, 11) (dual of [(16389, 4), 65471, 12]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(283, 16388, F2, 4, 10) (dual of [(16388, 4), 65469, 11]-NRT-code) | [i] | Truncation for OOAs | |
| 3 | Linear OOA(284, 16389, F2, 5, 11) (dual of [(16389, 5), 81861, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(284, 16389, F2, 6, 11) (dual of [(16389, 6), 98250, 12]-NRT-code) | [i] | ||
| 5 | Linear OOA(284, 16389, F2, 7, 11) (dual of [(16389, 7), 114639, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(284, 16389, F2, 8, 11) (dual of [(16389, 8), 131028, 12]-NRT-code) | [i] | ||
| 7 | Digital (73, 84, 16389)-net over F2 | [i] | ||