Information on Result #675145
Linear OA(3113, 19705, F3, 19) (dual of [19705, 19592, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
- linear OA(3109, 19683, F3, 19) (dual of [19683, 19574, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(34, 22, F3, 2) (dual of [22, 18, 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
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(3114, 19706, F3, 19) (dual of [19706, 19592, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3113, 9852, F3, 2, 19) (dual of [(9852, 2), 19591, 20]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3113, 6568, F3, 3, 19) (dual of [(6568, 3), 19591, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(3113, 4926, F3, 4, 19) (dual of [(4926, 4), 19591, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(3113, 3941, F3, 5, 19) (dual of [(3941, 5), 19592, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(3113, 2189, F3, 19, 19) (dual of [(2189, 19), 41478, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |