Information on Result #1297356
Linear OA(2184, 331, F2, 46) (dual of [331, 147, 47]-code), using construction X with Varšamov bound based on
- linear OA(2180, 324, F2, 46) (dual of [324, 144, 47]-code), using
- 1 times truncation [i] based on linear OA(2181, 325, F2, 47) (dual of [325, 144, 48]-code), using
- concatenation of two codes [i] based on
- linear OA(1629, 65, F16, 23) (dual of [65, 36, 24]-code), using
- extended algebraic-geometric code AGe(F,41P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- extended algebraic-geometric code AGe(F,41P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, 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(1629, 65, F16, 23) (dual of [65, 36, 24]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2181, 325, F2, 47) (dual of [325, 144, 48]-code), using
- linear OA(2180, 327, F2, 44) (dual of [327, 147, 45]-code), using Gilbert–Varšamov bound and bm = 2180 > Vbs−1(k−1) = 1 256616 391052 743897 738992 933781 734855 241275 302905 277008 [i]
- linear OA(21, 4, F2, 1) (dual of [4, 3, 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(2185, 332, F2, 47) (dual of [332, 147, 48]-code) | [i] | Adding a Parity Check Bit | |