Information on Result #1321008
Linear OA(2113, 217, F2, 30) (dual of [217, 104, 31]-code), using construction X with Varšamov bound based on
- linear OA(299, 199, F2, 30) (dual of [199, 100, 31]-code), using
- a “TjhaiTomlinson†code from Grassl’s database [i]
- linear OA(299, 203, F2, 23) (dual of [203, 104, 24]-code), using Gilbert–Varšamov bound and bm = 299 > Vbs−1(k−1) = 161274 345205 763469 875077 388864 [i]
- linear OA(210, 14, F2, 6) (dual of [14, 4, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 15, F2, 6) (dual of [15, 5, 7]-code), using
- 1 times truncation [i] based on linear OA(211, 16, F2, 7) (dual of [16, 5, 8]-code), using
- Reed–Muller code RM(2,4) [i]
- 1 times truncation [i] based on linear OA(211, 16, F2, 7) (dual of [16, 5, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 15, F2, 6) (dual of [15, 5, 7]-code), using
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2114, 218, F2, 31) (dual of [218, 104, 32]-code) | [i] | Adding a Parity Check Bit | |