Information on Result #675637
Linear OA(3214, 6585, F3, 39) (dual of [6585, 6371, 40]-code), using construction XX applied to Ce(39) ⊂ Ce(36) ⊂ Ce(34) 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(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(31, 20, F3, 1) (dual of [20, 19, 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(31, 4, F3, 1) (dual of [4, 3, 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 (see above)
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(3214, 4053, F3, 2, 39) (dual of [(4053, 2), 7892, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3214, 4053, F3, 3, 39) (dual of [(4053, 3), 11945, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(3214, 4053, F3, 4, 39) (dual of [(4053, 4), 15998, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(3214, 4053, F3, 5, 39) (dual of [(4053, 5), 20051, 40]-NRT-code) | [i] | ||
| 5 | Digital (175, 214, 4053)-net over F3 | [i] | ||
| 6 | Linear OOA(3214, 3292, F3, 2, 39) (dual of [(3292, 2), 6370, 40]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3214, 2195, F3, 3, 39) (dual of [(2195, 3), 6371, 40]-NRT-code) | [i] | ||
| 8 | Linear OOA(3214, 1646, F3, 4, 39) (dual of [(1646, 4), 6370, 40]-NRT-code) | [i] | ||
| 9 | Linear OOA(3214, 1317, F3, 5, 39) (dual of [(1317, 5), 6371, 40]-NRT-code) | [i] | ||