Information on Result #678778
Linear OA(4185, 65600, F4, 29) (dual of [65600, 65415, 30]-code), using construction X applied to Ce(28) ⊂ Ce(20) based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
- an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
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(4185, 65600, F4, 28) (dual of [65600, 65415, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4186, 65601, F4, 29) (dual of [65601, 65415, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4187, 65602, F4, 29) (dual of [65602, 65415, 30]-code) | [i] | ||
| 4 | Linear OA(4188, 65603, F4, 29) (dual of [65603, 65415, 30]-code) | [i] | ||
| 5 | Linear OA(4189, 65604, F4, 29) (dual of [65604, 65415, 30]-code) | [i] | ||
| 6 | Linear OA(4184, 65599, F4, 28) (dual of [65599, 65415, 29]-code) | [i] | Truncation | |
| 7 | Linear OOA(4185, 46133, F4, 2, 29) (dual of [(46133, 2), 92081, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 8 | Linear OOA(4185, 46133, F4, 3, 29) (dual of [(46133, 3), 138214, 30]-NRT-code) | [i] | ||
| 9 | Digital (156, 185, 46133)-net over F4 | [i] | ||
| 10 | Linear OA(4187, 65603, F4, 29) (dual of [65603, 65416, 30]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OA(4188, 65605, F4, 29) (dual of [65605, 65417, 30]-code) | [i] | ||
| 12 | Linear OA(4189, 65607, F4, 29) (dual of [65607, 65418, 30]-code) | [i] | ||
| 13 | Linear OOA(4185, 32800, F4, 2, 29) (dual of [(32800, 2), 65415, 30]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(4185, 21866, F4, 3, 29) (dual of [(21866, 3), 65413, 30]-NRT-code) | [i] | ||