Information on Result #1052238
Linear OOA(2113, 1028, F2, 4, 19) (dual of [(1028, 4), 3999, 20]-NRT-code), using OOA 4-folding based on linear OA(2113, 4112, F2, 19) (dual of [4112, 3999, 20]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2110, 4109, F2, 19) (dual of [4109, 3999, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(297, 4096, F2, 17) (dual of [4096, 3999, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(18) ⊂ Ce(16) [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(2113, 1028, F2, 4, 18) (dual of [(1028, 4), 3999, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2114, 1028, F2, 4, 19) (dual of [(1028, 4), 3998, 20]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2112, 1027, F2, 4, 18) (dual of [(1027, 4), 3996, 19]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(2113, 1028, F2, 5, 19) (dual of [(1028, 5), 5027, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2113, 1028, F2, 6, 19) (dual of [(1028, 6), 6055, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(2113, 1028, F2, 7, 19) (dual of [(1028, 7), 7083, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(2113, 1028, F2, 8, 19) (dual of [(1028, 8), 8111, 20]-NRT-code) | [i] | ||
| 8 | Digital (94, 113, 1028)-net over F2 | [i] | ||