Information on Result #679221
Linear OA(4161, 16439, F4, 28) (dual of [16439, 16278, 29]-code), using construction X applied to Ce(28) ⊂ Ce(20) based on
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 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(4162, 16440, F4, 28) (dual of [16440, 16278, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4165, 16443, F4, 28) (dual of [16443, 16278, 29]-code) | [i] | ||
| 3 | Linear OOA(4161, 16439, F4, 2, 28) (dual of [(16439, 2), 32717, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4161, 16439, F4, 3, 28) (dual of [(16439, 3), 49156, 29]-NRT-code) | [i] | ||
| 5 | Digital (133, 161, 16439)-net over F4 | [i] | ||
| 6 | Linear OA(4162, 16441, F4, 28) (dual of [16441, 16279, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(4163, 16443, F4, 28) (dual of [16443, 16280, 29]-code) | [i] | ||
| 8 | Linear OOA(4161, 8219, F4, 2, 28) (dual of [(8219, 2), 16277, 29]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(4161, 5479, F4, 3, 28) (dual of [(5479, 3), 16276, 29]-NRT-code) | [i] | ||
| 10 | Linear OOA(4161, 1174, F4, 28, 28) (dual of [(1174, 28), 32711, 29]-NRT-code) | [i] | OA Folding and Stacking | |