Information on Result #677040
Linear OA(357, 738, F3, 14) (dual of [738, 681, 15]-code), using construction XX applied to Ce(13) ⊂ Ce(12) ⊂ Ce(10) based on
- linear OA(355, 729, F3, 14) (dual of [729, 674, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(349, 729, F3, 13) (dual of [729, 680, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(343, 729, F3, 11) (dual of [729, 686, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 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(357, 435, F3, 2, 14) (dual of [(435, 2), 813, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(357, 435, F3, 3, 14) (dual of [(435, 3), 1248, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(357, 435, F3, 4, 14) (dual of [(435, 4), 1683, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(357, 435, F3, 5, 14) (dual of [(435, 5), 2118, 15]-NRT-code) | [i] | ||
| 5 | Digital (43, 57, 435)-net over F3 | [i] | ||