Information on Result #812769
Linear OOA(351, 3286, F3, 2, 10) (dual of [(3286, 2), 6521, 11]-NRT-code), using OOA 2-folding based on linear OA(351, 6572, F3, 10) (dual of [6572, 6521, 11]-code), using
- construction XX applied to Ce(9) ⊂ Ce(7) ⊂ Ce(6) [i] based on
- linear OA(349, 6561, F3, 10) (dual of [6561, 6512, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(341, 6561, F3, 8) (dual of [6561, 6520, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(333, 6561, F3, 7) (dual of [6561, 6528, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(351, 3286, F3, 3, 10) (dual of [(3286, 3), 9807, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(351, 3286, F3, 4, 10) (dual of [(3286, 4), 13093, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(351, 3286, F3, 5, 10) (dual of [(3286, 5), 16379, 11]-NRT-code) | [i] | ||
| 4 | Digital (41, 51, 3286)-net over F3 | [i] | ||