Information on Result #945502
Linear OOA(284, 692, F2, 3, 15) (dual of [(692, 3), 1992, 16]-NRT-code), using OOA 3-folding based on linear OA(284, 2076, F2, 15) (dual of [2076, 1992, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(278, 2048, F2, 15) (dual of [2048, 1970, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(256, 2048, F2, 11) (dual of [2048, 1992, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(284, 692, F2, 4, 15) (dual of [(692, 4), 2684, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(284, 692, F2, 5, 15) (dual of [(692, 5), 3376, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(284, 692, F2, 6, 15) (dual of [(692, 6), 4068, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(284, 692, F2, 7, 15) (dual of [(692, 7), 4760, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(284, 692, F2, 8, 15) (dual of [(692, 8), 5452, 16]-NRT-code) | [i] | ||
| 6 | Digital (69, 84, 692)-net over F2 | [i] | ||