Information on Result #813553
Linear OOA(3101, 3290, F3, 2, 19) (dual of [(3290, 2), 6479, 20]-NRT-code), using OOA 2-folding based on linear OA(3101, 6580, F3, 19) (dual of [6580, 6479, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3101, 6581, F3, 19) (dual of [6581, 6480, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(397, 6561, F3, 19) (dual of [6561, 6464, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(381, 6561, F3, 16) (dual of [6561, 6480, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
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(3101, 3031, F3, 3, 19) (dual of [(3031, 3), 8992, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3101, 3031, F3, 4, 19) (dual of [(3031, 4), 12023, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(3101, 3031, F3, 5, 19) (dual of [(3031, 5), 15054, 20]-NRT-code) | [i] | ||
| 4 | Digital (82, 101, 3031)-net over F3 | [i] | ||