Information on Result #679171
Linear OA(4113, 16419, F4, 20) (dual of [16419, 16306, 21]-code), using construction X applied to Ce(20) ⊂ Ce(14) based on
- 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(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 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(4114, 16420, F4, 20) (dual of [16420, 16306, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4113, 14019, F4, 2, 20) (dual of [(14019, 2), 27925, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4113, 14019, F4, 3, 20) (dual of [(14019, 3), 41944, 21]-NRT-code) | [i] | ||
| 4 | Digital (93, 113, 14019)-net over F4 | [i] | ||
| 5 | Linear OA(4115, 16422, F4, 20) (dual of [16422, 16307, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4113, 8209, F4, 2, 20) (dual of [(8209, 2), 16305, 21]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4113, 5473, F4, 3, 20) (dual of [(5473, 3), 16306, 21]-NRT-code) | [i] | ||