Information on Result #1297318
Linear OA(2165, 322, F2, 40) (dual of [322, 157, 41]-code), using construction X with Varšamov bound based on
- linear OA(2162, 317, F2, 40) (dual of [317, 155, 41]-code), using
- 1 times truncation [i] based on linear OA(2163, 318, F2, 41) (dual of [318, 155, 42]-code), using
- concatenation of two codes [i] based on
- linear OA(3222, 53, F32, 20) (dual of [53, 31, 21]-code), using
- extended algebraic-geometric code AGe(F,32P) [i] based on function field F/F32 with g(F) = 2 and N(F) ≥ 53, 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(3222, 53, F32, 20) (dual of [53, 31, 21]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2163, 318, F2, 41) (dual of [318, 155, 42]-code), using
- linear OA(2162, 319, F2, 38) (dual of [319, 157, 39]-code), using Gilbert–Varšamov bound and bm = 2162 > Vbs−1(k−1) = 3 675748 429617 759618 789776 362793 797447 201434 298015 [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(2166, 323, F2, 41) (dual of [323, 157, 42]-code) | [i] | Adding a Parity Check Bit | |