Information on Result #1096377
Linear OOA(2181, 6556, F2, 5, 24) (dual of [(6556, 5), 32599, 25]-NRT-code), using OOA 5-folding based on linear OA(2181, 32780, F2, 24) (dual of [32780, 32599, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2181, 32783, F2, 24) (dual of [32783, 32602, 25]-code), using
- 1 times truncation [i] based on linear OA(2182, 32784, F2, 25) (dual of [32784, 32602, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2181, 32768, F2, 25) (dual of [32768, 32587, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(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(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2182, 32784, F2, 25) (dual of [32784, 32602, 26]-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(2181, 6556, F2, 6, 24) (dual of [(6556, 6), 39155, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2181, 6556, F2, 7, 24) (dual of [(6556, 7), 45711, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(2181, 6556, F2, 8, 24) (dual of [(6556, 8), 52267, 25]-NRT-code) | [i] | ||
| 4 | Digital (157, 181, 6556)-net over F2 | [i] | ||