Information on Result #2661679
Linear OOA(3217, 531456, F3, 3, 24) (dual of [(531456, 3), 1594151, 25]-NRT-code), using 1 step truncation based on linear OOA(3218, 531457, F3, 3, 25) (dual of [(531457, 3), 1594153, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3218, 1594371, F3, 25) (dual of [1594371, 1594153, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3209, 1594323, F3, 25) (dual of [1594323, 1594114, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(39, 48, F3, 4) (dual of [48, 39, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [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(3217, 529003, F3, 4, 24) (dual of [(529003, 4), 2115795, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3217, 529003, F3, 5, 24) (dual of [(529003, 5), 2644798, 25]-NRT-code) | [i] | ||
| 3 | Digital (193, 217, 529003)-net over F3 | [i] | ||