Information on Result #2226873
Linear OA(2250, 454, F2, 62) (dual of [454, 204, 63]-code), using 1 times truncation based on linear OA(2251, 455, F2, 63) (dual of [455, 204, 64]-code), using
- concatenation of two codes [i] based on
- linear OA(6431, 65, F64, 31) (dual of [65, 34, 32]-code or 65-arc in PG(30,64)), using
- extended Reed–Solomon code RSe(34,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(21, 7, F2, 1) (dual of [7, 6, 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
- linear OA(6431, 65, F64, 31) (dual of [65, 34, 32]-code or 65-arc in PG(30,64)), 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 OA(2252, 456, F2, 62) (dual of [456, 204, 63]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2253, 457, F2, 62) (dual of [457, 204, 63]-code) | [i] | ||
| 3 | Linear OA(2254, 458, F2, 62) (dual of [458, 204, 63]-code) | [i] | ||
| 4 | Linear OA(2255, 459, F2, 62) (dual of [459, 204, 63]-code) | [i] | ||
| 5 | Linear OA(2256, 460, F2, 62) (dual of [460, 204, 63]-code) | [i] | ||
| 6 | Linear OA(2257, 461, F2, 62) (dual of [461, 204, 63]-code) | [i] | ||
| 7 | Linear OA(2255, 464, F2, 62) (dual of [464, 209, 63]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(2256, 467, F2, 62) (dual of [467, 211, 63]-code) | [i] | ||
| 9 | Linear OA(2257, 470, F2, 62) (dual of [470, 213, 63]-code) | [i] | ||
| 10 | Linear OA(2258, 474, F2, 62) (dual of [474, 216, 63]-code) | [i] | ||
| 11 | Linear OA(2252, 457, F2, 62) (dual of [457, 205, 63]-code) | [i] | Construction X with Varšamov Bound | |
| 12 | Linear OA(2253, 459, F2, 62) (dual of [459, 206, 63]-code) | [i] | ||
| 13 | Linear OA(2254, 461, F2, 62) (dual of [461, 207, 63]-code) | [i] | ||
| 14 | Linear OA(2255, 463, F2, 62) (dual of [463, 208, 63]-code) | [i] | ||
| 15 | Linear OA(2256, 465, F2, 62) (dual of [465, 209, 63]-code) | [i] | ||
| 16 | Linear OOA(2250, 227, F2, 2, 62) (dual of [(227, 2), 204, 63]-NRT-code) | [i] | OOA Folding | |
| 17 | Linear OOA(2250, 151, F2, 3, 62) (dual of [(151, 3), 203, 63]-NRT-code) | [i] | ||