Information on Result #808123
Linear OOA(2176, 526, F2, 2, 35) (dual of [(526, 2), 876, 36]-NRT-code), using OOA 2-folding based on linear OA(2176, 1052, F2, 35) (dual of [1052, 876, 36]-code), using
- construction XX applied to Ce(34) ⊂ Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2166, 1024, F2, 35) (dual of [1024, 858, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2151, 1024, F2, 31) (dual of [1024, 873, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2141, 1024, F2, 29) (dual of [1024, 883, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- linear OA(21, 4, F2, 1) (dual of [4, 3, 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
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(2176, 510, F2, 3, 35) (dual of [(510, 3), 1354, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2176, 510, F2, 4, 35) (dual of [(510, 4), 1864, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(2176, 510, F2, 5, 35) (dual of [(510, 5), 2374, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(2176, 510, F2, 6, 35) (dual of [(510, 6), 2884, 36]-NRT-code) | [i] | ||
| 5 | Linear OOA(2176, 510, F2, 7, 35) (dual of [(510, 7), 3394, 36]-NRT-code) | [i] | ||
| 6 | Linear OOA(2176, 510, F2, 8, 35) (dual of [(510, 8), 3904, 36]-NRT-code) | [i] | ||
| 7 | Digital (141, 176, 510)-net over F2 | [i] | ||