Information on Result #1321004
Linear OA(2110, 212, F2, 30) (dual of [212, 102, 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, 201, F2, 23) (dual of [201, 102, 24]-code), using Gilbert–Varšamov bound and bm = 299 > Vbs−1(k−1) = 128175 298003 429376 334631 996316 [i]
- linear OA(29, 11, F2, 6) (dual of [11, 2, 7]-code), using
- 1 times truncation [i] based on linear OA(210, 12, F2, 7) (dual of [12, 2, 8]-code), using
- repeating each code word 4 times [i] based on 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, using
- repeating each code word 4 times [i] based on linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), using
- 1 times truncation [i] based on linear OA(210, 12, F2, 7) (dual of [12, 2, 8]-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(2111, 213, F2, 31) (dual of [213, 102, 32]-code) | [i] | Adding a Parity Check Bit | |