Information on Result #677043
Linear OA(345, 738, F3, 11) (dual of [738, 693, 12]-code), using construction XX applied to Ce(10) ⊂ Ce(9) ⊂ Ce(7) based on
- 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(337, 729, F3, 10) (dual of [729, 692, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(331, 729, F3, 8) (dual of [729, 698, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(345, 438, F3, 2, 11) (dual of [(438, 2), 831, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(345, 438, F3, 3, 11) (dual of [(438, 3), 1269, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(345, 438, F3, 4, 11) (dual of [(438, 4), 1707, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(345, 438, F3, 5, 11) (dual of [(438, 5), 2145, 12]-NRT-code) | [i] | ||
| 5 | Digital (34, 45, 438)-net over F3 | [i] | ||