Information on Result #1053664
Linear OOA(2199, 2052, F2, 4, 31) (dual of [(2052, 4), 8009, 32]-NRT-code), using OOA 4-folding based on linear OA(2199, 8208, F2, 31) (dual of [8208, 8009, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2197, 8206, F2, 31) (dual of [8206, 8009, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2183, 8192, F2, 29) (dual of [8192, 8009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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(30) ⊂ Ce(28) [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(2200, 2052, F2, 4, 31) (dual of [(2052, 4), 8008, 32]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2201, 2052, F2, 4, 31) (dual of [(2052, 4), 8007, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(2198, 2051, F2, 4, 30) (dual of [(2051, 4), 8006, 31]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(2199, 1872, F2, 5, 31) (dual of [(1872, 5), 9161, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2199, 1872, F2, 6, 31) (dual of [(1872, 6), 11033, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2199, 1872, F2, 7, 31) (dual of [(1872, 7), 12905, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2199, 1872, F2, 8, 31) (dual of [(1872, 8), 14777, 32]-NRT-code) | [i] | ||
| 8 | Digital (168, 199, 1872)-net over F2 | [i] | ||