Information on Result #2799087
Linear OOA(3242, 1195746, F3, 4, 26) (dual of [(1195746, 4), 4782742, 27]-NRT-code), using 32 times duplication based on linear OOA(3240, 1195746, F3, 4, 26) (dual of [(1195746, 4), 4782744, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3240, 4782984, F3, 26) (dual of [4782984, 4782744, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3239, 4782983, F3, 26) (dual of [4782983, 4782744, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3239, 4782969, F3, 26) (dual of [4782969, 4782730, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3225, 4782969, F3, 25) (dual of [4782969, 4782744, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3239, 4782983, F3, 26) (dual of [4782983, 4782744, 27]-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 OOA(3242, 1108738, F3, 5, 26) (dual of [(1108738, 5), 5543448, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (216, 242, 1108738)-net over F3 | [i] | ||