Information on Result #1052744
Linear OOA(2137, 1028, F2, 4, 23) (dual of [(1028, 4), 3975, 24]-NRT-code), using OOA 4-folding based on linear OA(2137, 4112, F2, 23) (dual of [4112, 3975, 24]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2134, 4109, F2, 23) (dual of [4109, 3975, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(2137, 1028, F2, 4, 22) (dual of [(1028, 4), 3975, 23]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2138, 1028, F2, 4, 23) (dual of [(1028, 4), 3974, 24]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2136, 1027, F2, 4, 22) (dual of [(1027, 4), 3972, 23]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(2137, 1028, F2, 5, 23) (dual of [(1028, 5), 5003, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2137, 1028, F2, 6, 23) (dual of [(1028, 6), 6031, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(2137, 1028, F2, 7, 23) (dual of [(1028, 7), 7059, 24]-NRT-code) | [i] | ||
| 7 | Linear OOA(2137, 1028, F2, 8, 23) (dual of [(1028, 8), 8087, 24]-NRT-code) | [i] | ||
| 8 | Digital (114, 137, 1028)-net over F2 | [i] | ||