Information on Result #823800
Linear OOA(4114, 8196, F4, 2, 22) (dual of [(8196, 2), 16278, 23]-NRT-code), using OOA 2-folding based on linear OA(4114, 16392, F4, 22) (dual of [16392, 16278, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4113, 16391, F4, 22) (dual of [16391, 16278, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
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 OOA(4114, 8196, F4, 3, 22) (dual of [(8196, 3), 24474, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (92, 114, 8196)-net over F4 | [i] | ||