Information on Result #677923
Linear OA(4255, 4194327, F4, 31) (dual of [4194327, 4194072, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(4254, 4194304, F4, 31) (dual of [4194304, 4194050, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4232, 4194304, F4, 29) (dual of [4194304, 4194072, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(41, 23, F4, 1) (dual of [23, 22, 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: Constructive and 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 OA(4256, 4194328, F4, 31) (dual of [4194328, 4194072, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4257, 4194329, F4, 31) (dual of [4194329, 4194072, 32]-code) | [i] | ||
| 3 | Linear OA(4258, 4194330, F4, 31) (dual of [4194330, 4194072, 32]-code) | [i] | ||
| 4 | Linear OOA(4255, 2097163, F4, 2, 31) (dual of [(2097163, 2), 4194071, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4255, 1398109, F4, 3, 31) (dual of [(1398109, 3), 4194072, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(4255, 279621, F4, 31, 31) (dual of [(279621, 31), 8667996, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |