Information on Result #1297817
Linear OA(2259, 459, F2, 64) (dual of [459, 200, 65]-code), using construction X with Varšamov bound based on
- linear OA(2256, 454, F2, 64) (dual of [454, 198, 65]-code), using
- 1 times truncation [i] based on linear OA(2257, 455, F2, 65) (dual of [455, 198, 66]-code), using
- concatenation of two codes [i] based on
- linear OA(6432, 65, F64, 32) (dual of [65, 33, 33]-code or 65-arc in PG(31,64)), using
- extended Reed–Solomon code RSe(33,64) [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(6432, 65, F64, 32) (dual of [65, 33, 33]-code or 65-arc in PG(31,64)), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2257, 455, F2, 65) (dual of [455, 198, 66]-code), using
- linear OA(2256, 456, F2, 62) (dual of [456, 200, 63]-code), using Gilbert–Varšamov bound and bm = 2256 > Vbs−1(k−1) = 47427 580020 736178 232866 672018 229604 355668 816867 678597 608826 167283 651048 103104 [i]
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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 (see above)
Mode: 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(2260, 460, F2, 65) (dual of [460, 200, 66]-code) | [i] | Adding a Parity Check Bit | |