Information on Result #1053200
Linear OOA(2173, 2052, F2, 4, 27) (dual of [(2052, 4), 8035, 28]-NRT-code), using OOA 4-folding based on linear OA(2173, 8208, F2, 27) (dual of [8208, 8035, 28]-code), using
- 2 times code embedding in larger space [i] 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(2174, 2052, F2, 4, 27) (dual of [(2052, 4), 8034, 28]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2175, 2052, F2, 4, 27) (dual of [(2052, 4), 8033, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(2172, 2051, F2, 4, 26) (dual of [(2051, 4), 8032, 27]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(2173, 1827, F2, 5, 27) (dual of [(1827, 5), 8962, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2173, 1827, F2, 6, 27) (dual of [(1827, 6), 10789, 28]-NRT-code) | [i] | ||
| 6 | Linear OOA(2173, 1827, F2, 7, 27) (dual of [(1827, 7), 12616, 28]-NRT-code) | [i] | ||
| 7 | Linear OOA(2173, 1827, F2, 8, 27) (dual of [(1827, 8), 14443, 28]-NRT-code) | [i] | ||
| 8 | Digital (146, 173, 1827)-net over F2 | [i] | ||