Information on Result #945344
Linear OOA(268, 686, F2, 3, 13) (dual of [(686, 3), 1990, 14]-NRT-code), using OOA 3-folding based on linear OA(268, 2058, F2, 13) (dual of [2058, 1990, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(268, 2060, F2, 13) (dual of [2060, 1992, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(267, 2048, F2, 13) (dual of [2048, 1981, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(256, 2048, F2, 11) (dual of [2048, 1992, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(12) ⊂ Ce(10) [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(268, 607, F2, 4, 13) (dual of [(607, 4), 2360, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(268, 607, F2, 5, 13) (dual of [(607, 5), 2967, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(268, 607, F2, 6, 13) (dual of [(607, 6), 3574, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(268, 607, F2, 7, 13) (dual of [(607, 7), 4181, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(268, 607, F2, 8, 13) (dual of [(607, 8), 4788, 14]-NRT-code) | [i] | ||
| 6 | Digital (55, 68, 607)-net over F2 | [i] | ||