Information on Result #2263431
Linear OA(339, 19704, F3, 6) (dual of [19704, 19665, 7]-code), using 1 times code embedding in larger space based on linear OA(338, 19703, F3, 6) (dual of [19703, 19665, 7]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(337, 19683, F3, 7) (dual of [19683, 19646, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(319, 19683, F3, 4) (dual of [19683, 19664, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
- dual of repetition code with length 20 [i]
- linear OA(31, 20, F3, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(339, 9852, F3, 2, 6) (dual of [(9852, 2), 19665, 7]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(339, 6568, F3, 3, 6) (dual of [(6568, 3), 19665, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(339, 6568, F3, 4, 6) (dual of [(6568, 4), 26233, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 4 | Linear OOA(339, 6568, F3, 5, 6) (dual of [(6568, 5), 32801, 7]-NRT-code) | [i] | ||