Information on Result #679648
Linear OA(4100, 4111, F4, 22) (dual of [4111, 4011, 23]-code), using construction X applied to Ce(21) ⊂ Ce(18) based on
- linear OA(497, 4096, F4, 22) (dual of [4096, 3999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(485, 4096, F4, 19) (dual of [4096, 4011, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(43, 15, F4, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-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 OOA(4100, 2629, F4, 2, 22) (dual of [(2629, 2), 5158, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4100, 2629, F4, 3, 22) (dual of [(2629, 3), 7787, 23]-NRT-code) | [i] | ||
| 3 | Digital (78, 100, 2629)-net over F4 | [i] | ||
| 4 | Linear OOA(4100, 2055, F4, 2, 22) (dual of [(2055, 2), 4010, 23]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4100, 1370, F4, 3, 22) (dual of [(1370, 3), 4010, 23]-NRT-code) | [i] | ||