Information on Result #675456
Linear OA(3212, 6574, F3, 40) (dual of [6574, 6362, 41]-code), using construction X applied to Ce(39) ⊂ Ce(36) 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(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(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [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(3212, 3314, F3, 2, 40) (dual of [(3314, 2), 6416, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3212, 3314, F3, 3, 40) (dual of [(3314, 3), 9730, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(3212, 3314, F3, 4, 40) (dual of [(3314, 4), 13044, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(3212, 3314, F3, 5, 40) (dual of [(3314, 5), 16358, 41]-NRT-code) | [i] | ||
| 5 | Digital (172, 212, 3314)-net over F3 | [i] | ||
| 6 | Linear OOA(3212, 3287, F3, 2, 40) (dual of [(3287, 2), 6362, 41]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3212, 2191, F3, 3, 40) (dual of [(2191, 3), 6361, 41]-NRT-code) | [i] | ||