Information on Result #737142
Linear OA(4245, 4194372, F4, 29) (dual of [4194372, 4194127, 30]-code), using construction X applied to Ce(28) ⊂ Ce(21) based on
- 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(4177, 4194304, F4, 22) (dual of [4194304, 4194127, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(413, 68, F4, 6) (dual of [68, 55, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 70, F4, 6) (dual of [70, 57, 7]-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(4246, 4194373, F4, 29) (dual of [4194373, 4194127, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4247, 4194374, F4, 29) (dual of [4194374, 4194127, 30]-code) | [i] | ||
| 3 | Linear OA(4249, 4194376, F4, 29) (dual of [4194376, 4194127, 30]-code) | [i] | ||
| 4 | Linear OA(4249, 4194377, F4, 29) (dual of [4194377, 4194128, 30]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(4245, 2097186, F4, 2, 29) (dual of [(2097186, 2), 4194127, 30]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4245, 1398124, F4, 3, 29) (dual of [(1398124, 3), 4194127, 30]-NRT-code) | [i] | ||