Information on Result #699138
Linear OA(8142, 531465, F81, 13) (dual of [531465, 531423, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,3]) based on
- linear OA(8137, 531442, F81, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(8119, 531442, F81, 7) (dual of [531442, 531423, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(815, 23, F81, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), 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(8142, 531465, F81, 2, 13) (dual of [(531465, 2), 1062888, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8142, 531465, F81, 3, 13) (dual of [(531465, 3), 1594353, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(8142, 531465, F81, 4, 13) (dual of [(531465, 4), 2125818, 14]-NRT-code) | [i] | ||
| 4 | Digital (29, 42, 531465)-net over F81 | [i] | ||
| 5 | Linear OOA(8142, 265732, F81, 2, 13) (dual of [(265732, 2), 531422, 14]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8142, 177155, F81, 3, 13) (dual of [(177155, 3), 531423, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(8142, 132866, F81, 4, 13) (dual of [(132866, 4), 531422, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(8142, 88577, F81, 13, 13) (dual of [(88577, 13), 1151459, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |