Information on Result #815259
Linear OOA(3169, 3284, F3, 2, 32) (dual of [(3284, 2), 6399, 33]-NRT-code), using OOA 2-folding based on linear OA(3169, 6568, F3, 32) (dual of [6568, 6399, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3169, 6569, F3, 32) (dual of [6569, 6400, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(30, 8, F3, 0) (dual of [8, 8, 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(31) ⊂ Ce(30) [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(3169, 3235, F3, 3, 32) (dual of [(3235, 3), 9536, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3169, 3235, F3, 4, 32) (dual of [(3235, 4), 12771, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3169, 3235, F3, 5, 32) (dual of [(3235, 5), 16006, 33]-NRT-code) | [i] | ||
| 4 | Digital (137, 169, 3235)-net over F3 | [i] | ||