Information on Result #962047
Linear OOA(4171, 1398114, F4, 3, 21) (dual of [(1398114, 3), 4194171, 22]-NRT-code), using OOA 3-folding based on linear OA(4171, 4194342, F4, 21) (dual of [4194342, 4194171, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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 OOA(4174, 1398115, F4, 3, 21) (dual of [(1398115, 3), 4194171, 22]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4172, 1398114, F4, 3, 21) (dual of [(1398114, 3), 4194170, 22]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(4173, 1398114, F4, 3, 21) (dual of [(1398114, 3), 4194169, 22]-NRT-code) | [i] | ||
| 4 | Digital (150, 171, 1398114)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |