Information on Result #675073
Linear OA(3118, 19729, F3, 18) (dual of [19729, 19611, 19]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- linear OA(3109, 19684, F3, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(373, 19684, F3, 13) (dual of [19684, 19611, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 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(3118, 10467, F3, 2, 18) (dual of [(10467, 2), 20816, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3118, 10467, F3, 3, 18) (dual of [(10467, 3), 31283, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(3118, 10467, F3, 4, 18) (dual of [(10467, 4), 41750, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(3118, 10467, F3, 5, 18) (dual of [(10467, 5), 52217, 19]-NRT-code) | [i] | ||
| 5 | Digital (100, 118, 10467)-net over F3 | [i] | ||
| 6 | Linear OOA(3118, 9864, F3, 2, 18) (dual of [(9864, 2), 19610, 19]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3118, 6576, F3, 3, 18) (dual of [(6576, 3), 19610, 19]-NRT-code) | [i] | ||
| 8 | Linear OOA(3118, 4932, F3, 4, 18) (dual of [(4932, 4), 19610, 19]-NRT-code) | [i] | ||
| 9 | Linear OOA(3118, 2192, F3, 18, 18) (dual of [(2192, 18), 39338, 19]-NRT-code) | [i] | OA Folding and Stacking | |