Information on Result #679640
Linear OA(4140, 4109, F4, 31) (dual of [4109, 3969, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(4139, 4096, F4, 31) (dual of [4096, 3957, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 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(4141, 4110, F4, 31) (dual of [4110, 3969, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4140, 2968, F4, 2, 31) (dual of [(2968, 2), 5796, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4140, 2968, F4, 3, 31) (dual of [(2968, 3), 8764, 32]-NRT-code) | [i] | ||
| 4 | Digital (109, 140, 2968)-net over F4 | [i] | ||
| 5 | Linear OOA(4140, 2054, F4, 2, 31) (dual of [(2054, 2), 3968, 32]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4140, 1369, F4, 3, 31) (dual of [(1369, 3), 3967, 32]-NRT-code) | [i] | ||