Information on Result #816261
Linear OOA(3211, 3286, F3, 2, 40) (dual of [(3286, 2), 6361, 41]-NRT-code), using OOA 2-folding based on linear OA(3211, 6572, F3, 40) (dual of [6572, 6361, 41]-code), using
- construction XX applied to Ce(39) ⊂ Ce(37) ⊂ Ce(36) [i] based on
- linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(3211, 3286, F3, 3, 40) (dual of [(3286, 3), 9647, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3211, 3286, F3, 4, 40) (dual of [(3286, 4), 12933, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(3211, 3286, F3, 5, 40) (dual of [(3286, 5), 16219, 41]-NRT-code) | [i] | ||
| 4 | Digital (171, 211, 3286)-net over F3 | [i] | ||