Information on Result #1297791
Linear OA(2257, 390, F2, 70) (dual of [390, 133, 71]-code), using construction X with Varšamov bound based on
- linear OA(2253, 383, F2, 70) (dual of [383, 130, 71]-code), using
- 1 times truncation [i] based on linear OA(2254, 384, F2, 71) (dual of [384, 130, 72]-code), using
- concatenation of two codes [i] based on
- linear OA(3238, 64, F32, 35) (dual of [64, 26, 36]-code), using
- extended algebraic-geometric code AGe(F,28P) [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(3238, 64, F32, 35) (dual of [64, 26, 36]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2254, 384, F2, 71) (dual of [384, 130, 72]-code), using
- linear OA(2253, 386, F2, 68) (dual of [386, 133, 69]-code), using Gilbert–Varšamov bound and bm = 2253 > Vbs−1(k−1) = 13008 272224 622639 902731 545995 437874 494860 389063 556133 740421 315884 768512 715054 [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(2258, 391, F2, 71) (dual of [391, 133, 72]-code) | [i] | Adding a Parity Check Bit | |