Information on Result #1131724
Linear OOA(2186, 174767, F2, 6, 19) (dual of [(174767, 6), 1048416, 20]-NRT-code), using OOA 6-folding based on linear OA(2186, 1048602, F2, 19) (dual of [1048602, 1048416, 20]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2182, 1048598, F2, 19) (dual of [1048598, 1048416, 20]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2181, 1048576, F2, 19) (dual of [1048576, 1048395, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2161, 1048576, F2, 17) (dual of [1048576, 1048415, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(221, 22, F2, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
- dual of repetition code with length 22 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 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 X4 applied to Ce(18) ⊂ Ce(16) [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(2185, 174766, F2, 6, 18) (dual of [(174766, 6), 1048411, 19]-NRT-code) | [i] | Truncation for OOAs | |
| 2 | Linear OOA(2186, 173288, F2, 7, 19) (dual of [(173288, 7), 1212830, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2186, 173288, F2, 8, 19) (dual of [(173288, 8), 1386118, 20]-NRT-code) | [i] | ||
| 4 | Digital (167, 186, 173288)-net over F2 | [i] | ||