Information on Result #2921927
Linear OOA(2251, 174771, F2, 6, 24) (dual of [(174771, 6), 1048375, 25]-NRT-code), using 21 times duplication based on linear OOA(2250, 174771, F2, 6, 24) (dual of [(174771, 6), 1048376, 25]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2250, 1048626, F2, 24) (dual of [1048626, 1048376, 25]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2247, 1048623, F2, 24) (dual of [1048623, 1048376, 25]-code), using
- 1 times truncation [i] based on linear OA(2248, 1048624, F2, 25) (dual of [1048624, 1048376, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2241, 1048577, F2, 25) (dual of [1048577, 1048336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2201, 1048577, F2, 21) (dual of [1048577, 1048376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 47, F2, 3) (dual of [47, 40, 4]-code or 47-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- 1 times truncation [i] based on linear OA(2248, 1048624, F2, 25) (dual of [1048624, 1048376, 26]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2247, 1048623, F2, 24) (dual of [1048623, 1048376, 25]-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(2251, 156405, F2, 7, 24) (dual of [(156405, 7), 1094584, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2251, 156405, F2, 8, 24) (dual of [(156405, 8), 1250989, 25]-NRT-code) | [i] | ||
| 3 | Digital (227, 251, 156405)-net over F2 | [i] | ||