Information on Result #1297757
Linear OA(2252, 428, F2, 64) (dual of [428, 176, 65]-code), using construction X with Varšamov bound based on
- linear OA(2250, 425, F2, 64) (dual of [425, 175, 65]-code), using
- 1 times truncation [i] based on linear OA(2251, 426, F2, 65) (dual of [426, 175, 66]-code), using
- concatenation of two codes [i] based on
- linear OA(3236, 71, F32, 32) (dual of [71, 35, 33]-code), using
- extended algebraic-geometric code AGe(F,38P) [i] based on function field F/F32 with g(F) = 4 and N(F) ≥ 71, using
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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(3236, 71, F32, 32) (dual of [71, 35, 33]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2251, 426, F2, 65) (dual of [426, 175, 66]-code), using
- linear OA(2250, 426, F2, 62) (dual of [426, 176, 63]-code), using Gilbert–Varšamov bound and bm = 2250 > Vbs−1(k−1) = 549 088266 357759 621674 527494 221850 912855 831269 372457 573760 795955 089279 035424 [i]
- linear OA(21, 2, F2, 1) (dual of [2, 1, 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(2253, 429, F2, 65) (dual of [429, 176, 66]-code) | [i] | Adding a Parity Check Bit | |