Information on Result #675632
Linear OA(3219, 6572, F3, 41) (dual of [6572, 6353, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(39) ⊂ Ce(37) based on
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- 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(30, 9, F3, 0) (dual of [9, 9, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(3219, 3539, F3, 2, 41) (dual of [(3539, 2), 6859, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3219, 3539, F3, 3, 41) (dual of [(3539, 3), 10398, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3219, 3539, F3, 4, 41) (dual of [(3539, 4), 13937, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3219, 3539, F3, 5, 41) (dual of [(3539, 5), 17476, 42]-NRT-code) | [i] | ||
| 5 | Digital (178, 219, 3539)-net over F3 | [i] | ||
| 6 | Linear OOA(3219, 3286, F3, 2, 41) (dual of [(3286, 2), 6353, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3219, 1643, F3, 4, 41) (dual of [(1643, 4), 6353, 42]-NRT-code) | [i] | ||