Information on Result #1297557
Linear OA(2227, 389, F2, 58) (dual of [389, 162, 59]-code), using construction X with Varšamov bound based on
- linear OA(2224, 384, F2, 59) (dual of [384, 160, 60]-code), using
- concatenation of two codes [i] based on
- linear OA(3232, 64, F32, 29) (dual of [64, 32, 30]-code), using
- extended algebraic-geometric code AGe(F,34P) [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, 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(3232, 64, F32, 29) (dual of [64, 32, 30]-code), using
- concatenation of two codes [i] based on
- linear OA(2224, 386, F2, 56) (dual of [386, 162, 57]-code), using Gilbert–Varšamov bound and bm = 2224 > Vbs−1(k−1) = 25 996790 703964 663402 632261 495339 801405 866939 568578 666763 345969 144074 [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(2228, 390, F2, 59) (dual of [390, 162, 60]-code) | [i] | Adding a Parity Check Bit | |