Information on Result #2266974
Linear OA(3244, 6620, F3, 43) (dual of [6620, 6376, 44]-code), using 3 times code embedding in larger space based on linear OA(3241, 6617, F3, 43) (dual of [6617, 6376, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(34) [i] based on
- linear OA(3225, 6561, F3, 43) (dual of [6561, 6336, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [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(316, 56, F3, 7) (dual of [56, 40, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
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(3244, 5389, F3, 2, 43) (dual of [(5389, 2), 10534, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3244, 5389, F3, 3, 43) (dual of [(5389, 3), 15923, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(3244, 5389, F3, 4, 43) (dual of [(5389, 4), 21312, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(3244, 5389, F3, 5, 43) (dual of [(5389, 5), 26701, 44]-NRT-code) | [i] | ||
| 5 | Digital (201, 244, 5389)-net over F3 | [i] | ||
| 6 | Linear OOA(3244, 1655, F3, 4, 43) (dual of [(1655, 4), 6376, 44]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3244, 1324, F3, 5, 43) (dual of [(1324, 5), 6376, 44]-NRT-code) | [i] | ||