Information on Result #946679
Linear OOA(2144, 686, F2, 3, 26) (dual of [(686, 3), 1914, 27]-NRT-code), using OOA 3-folding based on linear OA(2144, 2058, F2, 26) (dual of [2058, 1914, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2144, 2059, F2, 26) (dual of [2059, 1915, 27]-code), using
- 1 times truncation [i] based on linear OA(2145, 2060, F2, 27) (dual of [2060, 1915, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2133, 2048, F2, 25) (dual of [2048, 1915, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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(26) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2145, 2060, F2, 27) (dual of [2060, 1915, 28]-code), using
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(2144, 686, F2, 4, 26) (dual of [(686, 4), 2600, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2144, 686, F2, 5, 26) (dual of [(686, 5), 3286, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(2144, 686, F2, 6, 26) (dual of [(686, 6), 3972, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(2144, 686, F2, 7, 26) (dual of [(686, 7), 4658, 27]-NRT-code) | [i] | ||
| 5 | Linear OOA(2144, 686, F2, 8, 26) (dual of [(686, 8), 5344, 27]-NRT-code) | [i] | ||
| 6 | Digital (118, 144, 686)-net over F2 | [i] | ||