Information on Result #1096174
Linear OOA(2168, 6557, F2, 5, 22) (dual of [(6557, 5), 32617, 23]-NRT-code), using OOA 5-folding based on linear OA(2168, 32785, F2, 22) (dual of [32785, 32617, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2166, 32783, F2, 22) (dual of [32783, 32617, 23]-code), using
- 1 times truncation [i] based on linear OA(2167, 32784, F2, 23) (dual of [32784, 32617, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2166, 32768, F2, 23) (dual of [32768, 32602, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2151, 32768, F2, 21) (dual of [32768, 32617, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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 X applied to Ce(22) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2167, 32784, F2, 23) (dual of [32784, 32617, 24]-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(2169, 6557, F2, 5, 22) (dual of [(6557, 5), 32616, 23]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2170, 6557, F2, 5, 22) (dual of [(6557, 5), 32615, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(2168, 6557, F2, 6, 22) (dual of [(6557, 6), 39174, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2168, 6557, F2, 7, 22) (dual of [(6557, 7), 45731, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(2168, 6557, F2, 8, 22) (dual of [(6557, 8), 52288, 23]-NRT-code) | [i] | ||
| 6 | Digital (146, 168, 6557)-net over F2 | [i] | ||