Information on Result #1464072
Linear OOA(8166, 5355, F81, 2, 29) (dual of [(5355, 2), 10644, 30]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8166, 5355, F81, 29) (dual of [5355, 5289, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 6591, F81, 29) (dual of [6591, 6525, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,9]) [i] based on
- linear OA(8157, 6562, F81, 29) (dual of [6562, 6505, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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
- construction X applied to C([0,14]) ⊂ C([0,9]) [i] based on
Mode: 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(8166, 2677, F81, 3, 29) (dual of [(2677, 3), 7965, 30]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8166, 2677, F81, 4, 29) (dual of [(2677, 4), 10642, 30]-NRT-code) | [i] | ||