Information on Result #1053199
Linear OOA(2171, 2051, F2, 4, 27) (dual of [(2051, 4), 8033, 28]-NRT-code), using OOA 4-folding based on linear OA(2171, 8204, F2, 27) (dual of [8204, 8033, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2171, 8206, F2, 27) (dual of [8206, 8035, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2157, 8192, F2, 25) (dual of [8192, 8035, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(26) ⊂ Ce(24) [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(2171, 2051, F2, 4, 26) (dual of [(2051, 4), 8033, 27]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2172, 2051, F2, 4, 27) (dual of [(2051, 4), 8032, 28]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2171, 1714, F2, 5, 27) (dual of [(1714, 5), 8399, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2171, 1714, F2, 6, 27) (dual of [(1714, 6), 10113, 28]-NRT-code) | [i] | ||
| 5 | Linear OOA(2171, 1714, F2, 7, 27) (dual of [(1714, 7), 11827, 28]-NRT-code) | [i] | ||
| 6 | Linear OOA(2171, 1714, F2, 8, 27) (dual of [(1714, 8), 13541, 28]-NRT-code) | [i] | ||
| 7 | Digital (144, 171, 1714)-net over F2 | [i] | ||