Information on Result #2494762
Linear OOA(4107, 2097172, F4, 2, 13) (dual of [(2097172, 2), 4194237, 14]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4105, 2097171, F4, 2, 13) (dual of [(2097171, 2), 4194237, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4105, 4194342, F4, 13) (dual of [4194342, 4194237, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(467, 4194304, F4, 9) (dual of [4194304, 4194237, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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
- construction X applied to Ce(12) ⊂ Ce(8) [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(4108, 2097172, F4, 2, 13) (dual of [(2097172, 2), 4194236, 14]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(4107, 2097172, F4, 3, 13) (dual of [(2097172, 3), 6291409, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (94, 107, 2097172)-net over F4 | [i] | ||