Information on Result #737005
Linear OA(3241, 6617, F3, 43) (dual of [6617, 6376, 44]-code), using construction X applied to Ce(42) ⊂ Ce(34) 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 OA(3243, 6619, F3, 43) (dual of [6619, 6376, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3244, 6620, F3, 43) (dual of [6620, 6376, 44]-code) | [i] | ||
| 3 | Linear OA(3245, 6621, F3, 43) (dual of [6621, 6376, 44]-code) | [i] | ||
| 4 | Linear OA(3240, 6616, F3, 42) (dual of [6616, 6376, 43]-code) | [i] | Truncation | |
| 5 | Linear OOA(3241, 4970, F3, 2, 43) (dual of [(4970, 2), 9699, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3241, 4970, F3, 3, 43) (dual of [(4970, 3), 14669, 44]-NRT-code) | [i] | ||
| 7 | Linear OOA(3241, 4970, F3, 4, 43) (dual of [(4970, 4), 19639, 44]-NRT-code) | [i] | ||
| 8 | Linear OOA(3241, 4970, F3, 5, 43) (dual of [(4970, 5), 24609, 44]-NRT-code) | [i] | ||
| 9 | Digital (198, 241, 4970)-net over F3 | [i] | ||
| 10 | Linear OA(3244, 6621, F3, 43) (dual of [6621, 6377, 44]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OA(3245, 6623, F3, 43) (dual of [6623, 6378, 44]-code) | [i] | ||
| 12 | Linear OOA(3241, 3308, F3, 2, 43) (dual of [(3308, 2), 6375, 44]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(3241, 2205, F3, 3, 43) (dual of [(2205, 3), 6374, 44]-NRT-code) | [i] | ||
| 14 | Linear OOA(3241, 1654, F3, 4, 43) (dual of [(1654, 4), 6375, 44]-NRT-code) | [i] | ||
| 15 | Linear OOA(3241, 1323, F3, 5, 43) (dual of [(1323, 5), 6374, 44]-NRT-code) | [i] | ||