Information on Result #1297649
Linear OA(2240, 457, F2, 58) (dual of [457, 217, 59]-code), using construction X with Varšamov bound based on
- linear OA(2238, 454, F2, 58) (dual of [454, 216, 59]-code), using
- 1 times truncation [i] based on linear OA(2239, 455, F2, 59) (dual of [455, 216, 60]-code), using
- concatenation of two codes [i] based on
- linear OA(6429, 65, F64, 29) (dual of [65, 36, 30]-code or 65-arc in PG(28,64)), using
- extended Reed–Solomon code RSe(36,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(21, 7, F2, 1) (dual of [7, 6, 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(6429, 65, F64, 29) (dual of [65, 36, 30]-code or 65-arc in PG(28,64)), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2239, 455, F2, 59) (dual of [455, 216, 60]-code), using
- linear OA(2238, 455, F2, 56) (dual of [455, 217, 57]-code), using Gilbert–Varšamov bound and bm = 2238 > Vbs−1(k−1) = 414324 129751 886143 748225 733855 077549 513626 521343 160581 761163 007684 158112 [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(2241, 458, F2, 59) (dual of [458, 217, 60]-code) | [i] | Adding a Parity Check Bit | |