Information on Result #2666859
Linear OOA(283, 688, F2, 3, 15) (dual of [(688, 3), 1981, 16]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(280, 687, F2, 3, 15) (dual of [(687, 3), 1981, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(280, 2061, F2, 15) (dual of [2061, 1981, 16]-code), using
- 1 times code embedding in larger space [i] based on linear OA(279, 2060, F2, 15) (dual of [2060, 1981, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(278, 2048, F2, 15) (dual of [2048, 1970, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(14) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(279, 2060, F2, 15) (dual of [2060, 1981, 16]-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(283, 688, F2, 4, 15) (dual of [(688, 4), 2669, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(283, 688, F2, 5, 15) (dual of [(688, 5), 3357, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(283, 688, F2, 6, 15) (dual of [(688, 6), 4045, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(283, 688, F2, 7, 15) (dual of [(688, 7), 4733, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(283, 688, F2, 8, 15) (dual of [(688, 8), 5421, 16]-NRT-code) | [i] | ||
| 6 | Digital (68, 83, 688)-net over F2 | [i] | ||