Information on Result #1317981
Linear OA(537, 54, F5, 21) (dual of [54, 17, 22]-code), using construction X with Varšamov bound based on
- linear OA(535, 51, F5, 21) (dual of [51, 16, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(535, 52, F5, 21) (dual of [52, 17, 22]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(535, 52, F5, 21) (dual of [52, 17, 22]-code), using
- linear OA(535, 52, F5, 19) (dual of [52, 17, 20]-code), using Gilbert–Varšamov bound and bm = 535 > Vbs−1(k−1) = 2 205720 838209 052417 532605 [i]
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(538, 56, F5, 21) (dual of [56, 18, 22]-code) | [i] | Construction X with Varšamov Bound | |