Information on Result #1653590
Linear OOA(2236, 1677780, F2, 5, 18) (dual of [(1677780, 5), 8388664, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(229, 60, F2, 5, 9) (dual of [(60, 5), 271, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(229, 60, F2, 2, 9) (dual of [(60, 2), 91, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(229, 64, F2, 2, 9) (dual of [(64, 2), 99, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(229, 128, F2, 9) (dual of [128, 99, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 2-folding [i] based on linear OA(229, 128, F2, 9) (dual of [128, 99, 10]-code), using
- discarding factors / shortening the dual code based on linear OOA(229, 64, F2, 2, 9) (dual of [(64, 2), 99, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(229, 60, F2, 2, 9) (dual of [(60, 2), 91, 10]-NRT-code), using
- linear OOA(2207, 1677720, F2, 5, 18) (dual of [(1677720, 5), 8388393, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- OOA 5-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2236, 1677780, F2, 6, 18) (dual of [(1677780, 6), 10066444, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2236, 1677780, F2, 7, 18) (dual of [(1677780, 7), 11744224, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2236, 1677780, F2, 8, 18) (dual of [(1677780, 8), 13422004, 19]-NRT-code) | [i] | ||
| 4 | Digital (218, 236, 1677780)-net over F2 | [i] | ||