Information on Result #1321000
Linear OA(2105, 207, F2, 28) (dual of [207, 102, 29]-code), using construction X with Varšamov bound based on
- linear OA(297, 197, F2, 28) (dual of [197, 100, 29]-code), using
- 3 times truncation [i] based on linear OA(2100, 200, F2, 31) (dual of [200, 100, 32]-code), using
- adding a parity check bit [i] based on linear OA(299, 199, F2, 30) (dual of [199, 100, 31]-code), using
- a “TjhaiTomlinson†code from Grassl’s database [i]
- adding a parity check bit [i] based on linear OA(299, 199, F2, 30) (dual of [199, 100, 31]-code), using
- 3 times truncation [i] based on linear OA(2100, 200, F2, 31) (dual of [200, 100, 32]-code), using
- linear OA(297, 199, F2, 23) (dual of [199, 102, 24]-code), using Gilbert–Varšamov bound and bm = 297 > Vbs−1(k−1) = 101622 831934 337944 843481 984672 [i]
- linear OA(26, 8, F2, 4) (dual of [8, 2, 5]-code), using
- 1 times truncation [i] based on linear OA(27, 9, F2, 5) (dual of [9, 2, 6]-code), using
- repeating each code word 3 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 3 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(27, 9, F2, 5) (dual of [9, 2, 6]-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(2106, 208, F2, 29) (dual of [208, 102, 30]-code) | [i] | Adding a Parity Check Bit | |