Information on Result #679758
Linear OA(4140, 4127, F4, 30) (dual of [4127, 3987, 31]-code), using construction X applied to Ce(29) ⊂ Ce(24) based on
- linear OA(4133, 4096, F4, 30) (dual of [4096, 3963, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(47, 31, F4, 4) (dual of [31, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), 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, 4128, F4, 30) (dual of [4128, 3987, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4140, 3648, F4, 2, 30) (dual of [(3648, 2), 7156, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4140, 3648, F4, 3, 30) (dual of [(3648, 3), 10804, 31]-NRT-code) | [i] | ||
| 4 | Digital (110, 140, 3648)-net over F4 | [i] | ||
| 5 | Linear OA(4143, 4132, F4, 30) (dual of [4132, 3989, 31]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(4144, 4134, F4, 30) (dual of [4134, 3990, 31]-code) | [i] | ||
| 7 | Linear OA(4145, 4136, F4, 30) (dual of [4136, 3991, 31]-code) | [i] | ||
| 8 | Linear OOA(4140, 2063, F4, 2, 30) (dual of [(2063, 2), 3986, 31]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(4140, 1375, F4, 3, 30) (dual of [(1375, 3), 3985, 31]-NRT-code) | [i] | ||