Information on Result #1297366
Linear OA(2193, 331, F2, 50) (dual of [331, 138, 51]-code), using construction X with Varšamov bound based on
- linear OA(2188, 324, F2, 50) (dual of [324, 136, 51]-code), using
- 1 times truncation [i] based on linear OA(2189, 325, F2, 51) (dual of [325, 136, 52]-code), using
- concatenation of two codes [i] based on
- linear OA(1631, 65, F16, 25) (dual of [65, 34, 26]-code), using
- extended algebraic-geometric code AGe(F,39P) [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,39P) [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(1631, 65, F16, 25) (dual of [65, 34, 26]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2189, 325, F2, 51) (dual of [325, 136, 52]-code), using
- linear OA(2188, 326, F2, 47) (dual of [326, 138, 48]-code), using Gilbert–Varšamov bound and bm = 2188 > Vbs−1(k−1) = 269 804715 120678 697519 707492 774042 744117 460677 220497 581984 [i]
- linear OA(23, 5, F2, 2) (dual of [5, 2, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(23, 7, F2, 2) (dual of [7, 4, 3]-code), using
- Hamming code H(3,2) [i]
- discarding factors / shortening the dual code based on linear OA(23, 7, F2, 2) (dual of [7, 4, 3]-code), using
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(2194, 332, F2, 51) (dual of [332, 138, 52]-code) | [i] | Adding a Parity Check Bit | |