Information on Result #945898
Linear OOA(2117, 1376, F2, 3, 19) (dual of [(1376, 3), 4011, 20]-NRT-code), using OOA 3-folding based on linear OA(2117, 4128, F2, 19) (dual of [4128, 4011, 20]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2115, 4126, F2, 19) (dual of [4126, 4011, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [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(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [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(2116, 1375, F2, 3, 18) (dual of [(1375, 3), 4009, 19]-NRT-code) | [i] | Truncation for OOAs | |
| 2 | Linear OOA(2117, 1225, F2, 4, 19) (dual of [(1225, 4), 4783, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2117, 1225, F2, 5, 19) (dual of [(1225, 5), 6008, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(2117, 1225, F2, 6, 19) (dual of [(1225, 6), 7233, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(2117, 1225, F2, 7, 19) (dual of [(1225, 7), 8458, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(2117, 1225, F2, 8, 19) (dual of [(1225, 8), 9683, 20]-NRT-code) | [i] | ||
| 7 | Digital (98, 117, 1225)-net over F2 | [i] | ||