Information on Result #1653578
Linear OOA(2214, 1677789, F2, 5, 17) (dual of [(1677789, 5), 8388731, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(229, 69, F2, 5, 8) (dual of [(69, 5), 316, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(229, 69, F2, 8) (dual of [69, 40, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(229, 135, F2, 8) (dual of [135, 106, 9]-code), using
- 1 times truncation [i] based on linear OA(230, 136, F2, 9) (dual of [136, 106, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [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]
- linear OA(222, 128, F2, 7) (dual of [128, 106, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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(8) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(230, 136, F2, 9) (dual of [136, 106, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(229, 135, F2, 8) (dual of [135, 106, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(229, 69, F2, 8) (dual of [69, 40, 9]-code), using
- linear OOA(2185, 1677720, F2, 5, 17) (dual of [(1677720, 5), 8388415, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 5-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-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(2214, 1677789, F2, 6, 17) (dual of [(1677789, 6), 10066520, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2214, 1677789, F2, 7, 17) (dual of [(1677789, 7), 11744309, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(2214, 1677789, F2, 8, 17) (dual of [(1677789, 8), 13422098, 18]-NRT-code) | [i] | ||
| 4 | Digital (197, 214, 1677789)-net over F2 | [i] | ||