Information on Result #2788503
Linear OOA(2111, 8197, F2, 4, 15) (dual of [(8197, 4), 32677, 16]-NRT-code), using 21 times duplication based on linear OOA(2110, 8197, F2, 4, 15) (dual of [(8197, 4), 32678, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2110, 32788, F2, 15) (dual of [32788, 32678, 16]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2107, 32785, F2, 15) (dual of [32785, 32678, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2106, 32768, F2, 15) (dual of [32768, 32662, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(291, 32768, F2, 13) (dual of [32768, 32677, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(216, 17, F2, 15) (dual of [17, 1, 16]-code), using
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- dual of repetition code with length 17 [i]
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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(14) ⊂ Ce(12) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(2107, 32785, F2, 15) (dual of [32785, 32678, 16]-code), 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(2111, 7520, F2, 5, 15) (dual of [(7520, 5), 37489, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2111, 7520, F2, 6, 15) (dual of [(7520, 6), 45009, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(2111, 7520, F2, 7, 15) (dual of [(7520, 7), 52529, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(2111, 7520, F2, 8, 15) (dual of [(7520, 8), 60049, 16]-NRT-code) | [i] | ||
| 5 | Digital (96, 111, 7520)-net over F2 | [i] | ||