Information on Result #807474
Linear OOA(2166, 1042, F2, 2, 29) (dual of [(1042, 2), 1918, 30]-NRT-code), using OOA 2-folding based on linear OA(2166, 2084, F2, 29) (dual of [2084, 1918, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2166, 2085, F2, 29) (dual of [2085, 1919, 30]-code), using
- construction XX applied to Ce(28) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2155, 2048, F2, 29) (dual of [2048, 1893, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2133, 2048, F2, 25) (dual of [2048, 1915, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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 XX applied to Ce(28) ⊂ Ce(24) ⊂ Ce(22) [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(2166, 799, F2, 3, 29) (dual of [(799, 3), 2231, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2166, 799, F2, 4, 29) (dual of [(799, 4), 3030, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(2166, 799, F2, 5, 29) (dual of [(799, 5), 3829, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2166, 799, F2, 6, 29) (dual of [(799, 6), 4628, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(2166, 799, F2, 7, 29) (dual of [(799, 7), 5427, 30]-NRT-code) | [i] | ||
| 6 | Linear OOA(2166, 799, F2, 8, 29) (dual of [(799, 8), 6226, 30]-NRT-code) | [i] | ||
| 7 | Digital (137, 166, 799)-net over F2 | [i] | ||