Information on Result #1132157
Linear OOA(2193, 21849, F2, 6, 23) (dual of [(21849, 6), 130901, 24]-NRT-code), using OOA 6-folding based on linear OA(2193, 131094, F2, 23) (dual of [131094, 130901, 24]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2189, 131090, F2, 23) (dual of [131090, 130901, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2188, 131072, F2, 23) (dual of [131072, 130884, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2171, 131072, F2, 21) (dual of [131072, 130901, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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 X applied to Ce(22) ⊂ Ce(20) [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(2192, 21848, F2, 6, 22) (dual of [(21848, 6), 130896, 23]-NRT-code) | [i] | Truncation for OOAs | |
| 2 | Linear OOA(2193, 21849, F2, 7, 23) (dual of [(21849, 7), 152750, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2193, 21849, F2, 8, 23) (dual of [(21849, 8), 174599, 24]-NRT-code) | [i] | ||
| 4 | Digital (170, 193, 21849)-net over F2 | [i] | ||