Information on Result #2921702
Linear OOA(2225, 174766, F2, 6, 22) (dual of [(174766, 6), 1048371, 23]-NRT-code), using 24 times duplication based on linear OOA(2221, 174766, F2, 6, 22) (dual of [(174766, 6), 1048375, 23]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2221, 1048596, F2, 22) (dual of [1048596, 1048375, 23]-code), using
- 1 times truncation [i] based on linear OA(2222, 1048597, F2, 23) (dual of [1048597, 1048375, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2201, 1048576, F2, 21) (dual of [1048576, 1048375, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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(22) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2222, 1048597, F2, 23) (dual of [1048597, 1048375, 24]-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(2225, 159495, F2, 7, 22) (dual of [(159495, 7), 1116240, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2225, 159495, F2, 8, 22) (dual of [(159495, 8), 1275735, 23]-NRT-code) | [i] | ||
| 3 | Digital (203, 225, 159495)-net over F2 | [i] | ||