Information on Result #677038
Linear OA(365, 747, F3, 15) (dual of [747, 682, 16]-code), using construction XX applied to Ce(15) ⊂ Ce(12) ⊂ Ce(10) based on
- linear OA(361, 729, F3, 16) (dual of [729, 668, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(31, 15, F3, 1) (dual of [15, 14, 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, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [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(365, 621, F3, 2, 15) (dual of [(621, 2), 1177, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(365, 621, F3, 3, 15) (dual of [(621, 3), 1798, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(365, 621, F3, 4, 15) (dual of [(621, 4), 2419, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(365, 621, F3, 5, 15) (dual of [(621, 5), 3040, 16]-NRT-code) | [i] | ||
| 5 | Digital (50, 65, 621)-net over F3 | [i] | ||