Information on Result #678729
Linear OA(4208, 65575, F4, 34) (dual of [65575, 65367, 35]-code), using construction X applied to Ce(33) ⊂ Ce(28) based on
- linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(47, 39, F4, 4) (dual of [39, 32, 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(4209, 65576, F4, 34) (dual of [65576, 65367, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4210, 65577, F4, 34) (dual of [65577, 65367, 35]-code) | [i] | ||
| 3 | Linear OA(4211, 65578, F4, 34) (dual of [65578, 65367, 35]-code) | [i] | ||
| 4 | Linear OA(4212, 65579, F4, 34) (dual of [65579, 65367, 35]-code) | [i] | ||
| 5 | Linear OA(4213, 65580, F4, 34) (dual of [65580, 65367, 35]-code) | [i] | ||
| 6 | Linear OOA(4208, 33420, F4, 2, 34) (dual of [(33420, 2), 66632, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4208, 33420, F4, 3, 34) (dual of [(33420, 3), 100052, 35]-NRT-code) | [i] | ||
| 8 | Digital (174, 208, 33420)-net over F4 | [i] | ||
| 9 | Linear OA(4212, 65580, F4, 34) (dual of [65580, 65368, 35]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4213, 65582, F4, 34) (dual of [65582, 65369, 35]-code) | [i] | ||
| 11 | Linear OOA(4208, 32787, F4, 2, 34) (dual of [(32787, 2), 65366, 35]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(4208, 21858, F4, 3, 34) (dual of [(21858, 3), 65366, 35]-NRT-code) | [i] | ||
| 13 | Linear OOA(4208, 3857, F4, 34, 34) (dual of [(3857, 34), 130930, 35]-NRT-code) | [i] | OA Folding and Stacking | |