Information on Result #1308741
Linear OA(4226, 4323, F4, 49) (dual of [4323, 4097, 50]-code), using 212 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 9 times 0, 1, 18 times 0, 1, 34 times 0, 1, 57 times 0, 1, 82 times 0) based on linear OA(4218, 4103, F4, 49) (dual of [4103, 3885, 50]-code), using
- construction X applied to Ce(48) ⊂ Ce(46) [i] based on
- linear OA(4217, 4096, F4, 49) (dual of [4096, 3879, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(4211, 4096, F4, 47) (dual of [4096, 3885, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4226, 4323, F4, 2, 49) (dual of [(4323, 2), 8420, 50]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4226, 4323, F4, 3, 49) (dual of [(4323, 3), 12743, 50]-NRT-code) | [i] | ||
| 3 | Digital (177, 226, 4323)-net over F4 | [i] | ||