Information on Result #678784
Linear OA(4246, 65613, F4, 38) (dual of [65613, 65367, 39]-code), using construction X applied to Ce(37) ⊂ Ce(28) based on
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- 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(421, 77, F4, 8) (dual of [77, 56, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 84, F4, 8) (dual of [84, 63, 9]-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(4247, 65614, F4, 38) (dual of [65614, 65367, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4248, 65615, F4, 38) (dual of [65615, 65367, 39]-code) | [i] | ||
| 3 | Linear OA(4249, 65616, F4, 38) (dual of [65616, 65367, 39]-code) | [i] | ||
| 4 | Linear OA(4250, 65617, F4, 38) (dual of [65617, 65367, 39]-code) | [i] | ||
| 5 | Linear OOA(4246, 59533, F4, 2, 38) (dual of [(59533, 2), 118820, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(4246, 59533, F4, 3, 38) (dual of [(59533, 3), 178353, 39]-NRT-code) | [i] | ||
| 7 | Digital (208, 246, 59533)-net over F4 | [i] | ||
| 8 | Linear OA(4248, 65616, F4, 38) (dual of [65616, 65368, 39]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(4249, 65618, F4, 38) (dual of [65618, 65369, 39]-code) | [i] | ||
| 10 | Linear OA(4250, 65620, F4, 38) (dual of [65620, 65370, 39]-code) | [i] | ||
| 11 | Linear OOA(4246, 32806, F4, 2, 38) (dual of [(32806, 2), 65366, 39]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(4246, 21871, F4, 3, 38) (dual of [(21871, 3), 65367, 39]-NRT-code) | [i] | ||