Information on Result #1297797
Linear OA(2257, 362, F2, 74) (dual of [362, 105, 75]-code), using construction X with Varšamov bound based on
- linear OA(2255, 359, F2, 74) (dual of [359, 104, 75]-code), using
- 1 times truncation [i] based on linear OA(2256, 360, F2, 75) (dual of [360, 104, 76]-code), using
- concatenation of two codes [i] based on
- linear OA(1646, 72, F16, 37) (dual of [72, 26, 38]-code), using
- extended algebraic-geometric code AGe(F,34P) [i] based on function field F/F16 with g(F) = 9 and N(F) ≥ 72, using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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(1646, 72, F16, 37) (dual of [72, 26, 38]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2256, 360, F2, 75) (dual of [360, 104, 76]-code), using
- linear OA(2255, 360, F2, 72) (dual of [360, 105, 73]-code), using Gilbert–Varšamov bound and bm = 2255 > Vbs−1(k−1) = 23920 774105 834276 805881 075145 036003 572692 911740 298861 160043 171013 636229 245312 [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(2258, 363, F2, 75) (dual of [363, 105, 76]-code) | [i] | Adding a Parity Check Bit | |