Information on Result #1297725
Linear OA(2249, 362, F2, 70) (dual of [362, 113, 71]-code), using construction X with Varšamov bound based on
- linear OA(2247, 359, F2, 70) (dual of [359, 112, 71]-code), using
- 1 times truncation [i] based on linear OA(2248, 360, F2, 71) (dual of [360, 112, 72]-code), using
- concatenation of two codes [i] based on
- linear OA(1644, 72, F16, 35) (dual of [72, 28, 36]-code), using
- extended algebraic-geometric code AGe(F,36P) [i] based on function field F/F16 with g(F) = 9 and N(F) ≥ 72, 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(1644, 72, F16, 35) (dual of [72, 28, 36]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2248, 360, F2, 71) (dual of [360, 112, 72]-code), using
- linear OA(2247, 360, F2, 68) (dual of [360, 113, 69]-code), using Gilbert–Varšamov bound and bm = 2247 > Vbs−1(k−1) = 76 619763 209452 804713 612918 517890 459960 813086 811234 075954 726285 775412 482112 [i]
- linear OA(21, 2, F2, 1) (dual of [2, 1, 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(2250, 363, F2, 71) (dual of [363, 113, 72]-code) | [i] | Adding a Parity Check Bit | |