Information on Result #1131597
Linear OOA(2181, 174766, F2, 6, 18) (dual of [(174766, 6), 1048415, 19]-NRT-code), using OOA 6-folding based on linear OA(2181, 1048596, F2, 18) (dual of [1048596, 1048415, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2181, 1048597, F2, 18) (dual of [1048597, 1048416, 19]-code), using
- 1 times truncation [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
- 1 times truncation [i] based on linear OA(2182, 1048598, F2, 19) (dual of [1048598, 1048416, 20]-code), 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(2183, 174766, F2, 6, 18) (dual of [(174766, 6), 1048413, 19]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2184, 174766, F2, 6, 18) (dual of [(174766, 6), 1048412, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2181, 174766, F2, 7, 18) (dual of [(174766, 7), 1223181, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2181, 174766, F2, 8, 18) (dual of [(174766, 8), 1397947, 19]-NRT-code) | [i] | ||
| 5 | Digital (163, 181, 174766)-net over F2 | [i] | ||