Information on Result #674516
Linear OA(3154, 531499, F3, 18) (dual of [531499, 531345, 19]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(397, 531442, F3, 13) (dual of [531442, 531345, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(39, 57, F3, 4) (dual of [57, 48, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 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(3154, 265749, F3, 2, 18) (dual of [(265749, 2), 531344, 19]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3154, 177166, F3, 3, 18) (dual of [(177166, 3), 531344, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(3154, 132874, F3, 4, 18) (dual of [(132874, 4), 531342, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(3154, 106299, F3, 5, 18) (dual of [(106299, 5), 531341, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(3154, 59055, F3, 18, 18) (dual of [(59055, 18), 1062836, 19]-NRT-code) | [i] | OA Folding and Stacking | |