Information on Result #699351
Linear OA(8178, 6591, F81, 35) (dual of [6591, 6513, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,12]) based on
- linear OA(8169, 6562, F81, 35) (dual of [6562, 6493, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(819, 29, F81, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), using
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- Reed–Solomon code RS(72,81) [i]
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), 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(8178, 4655, F81, 2, 35) (dual of [(4655, 2), 9232, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8178, 4655, F81, 3, 35) (dual of [(4655, 3), 13887, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(8178, 4655, F81, 4, 35) (dual of [(4655, 4), 18542, 36]-NRT-code) | [i] | ||
| 4 | Digital (43, 78, 4655)-net over F81 | [i] | ||
| 5 | Linear OOA(8178, 3295, F81, 2, 35) (dual of [(3295, 2), 6512, 36]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8178, 2197, F81, 3, 35) (dual of [(2197, 3), 6513, 36]-NRT-code) | [i] | ||
| 7 | Linear OOA(8178, 1647, F81, 4, 35) (dual of [(1647, 4), 6510, 36]-NRT-code) | [i] | ||