Information on Result #675516
Linear OA(3217, 6593, F3, 40) (dual of [6593, 6376, 41]-code), using construction X applied to Ce(39) ⊂ Ce(34) based on
- linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [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(38, 32, F3, 4) (dual of [32, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3217, 3835, F3, 2, 40) (dual of [(3835, 2), 7453, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3217, 3835, F3, 3, 40) (dual of [(3835, 3), 11288, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(3217, 3835, F3, 4, 40) (dual of [(3835, 4), 15123, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(3217, 3835, F3, 5, 40) (dual of [(3835, 5), 18958, 41]-NRT-code) | [i] | ||
| 5 | Digital (177, 217, 3835)-net over F3 | [i] | ||
| 6 | Linear OOA(3217, 3296, F3, 2, 40) (dual of [(3296, 2), 6375, 41]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3217, 2197, F3, 3, 40) (dual of [(2197, 3), 6374, 41]-NRT-code) | [i] | ||
| 8 | Linear OOA(3217, 1648, F3, 4, 40) (dual of [(1648, 4), 6375, 41]-NRT-code) | [i] | ||
| 9 | Linear OOA(3217, 1318, F3, 5, 40) (dual of [(1318, 5), 6373, 41]-NRT-code) | [i] | ||