Information on Result #1297773
Linear OA(2254, 364, F2, 72) (dual of [364, 110, 73]-code), using construction X with Varšamov bound based on
- linear OA(2251, 359, F2, 72) (dual of [359, 108, 73]-code), using
- 1 times truncation [i] based on linear OA(2252, 360, F2, 73) (dual of [360, 108, 74]-code), using
- concatenation of two codes [i] based on
- linear OA(1645, 72, F16, 36) (dual of [72, 27, 37]-code), using
- extended algebraic-geometric code AGe(F,35P) [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(1645, 72, F16, 36) (dual of [72, 27, 37]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2252, 360, F2, 73) (dual of [360, 108, 74]-code), using
- linear OA(2251, 361, F2, 70) (dual of [361, 110, 71]-code), using Gilbert–Varšamov bound and bm = 2251 > Vbs−1(k−1) = 1733 577385 719010 864003 259770 843663 657383 375449 400238 914828 403868 974911 158809 [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(2255, 365, F2, 73) (dual of [365, 110, 74]-code) | [i] | Adding a Parity Check Bit | |