Information on Result #699566
Linear OA(8182, 6584, F81, 38) (dual of [6584, 6502, 39]-code), using construction X applied to Ce(37) ⊂ Ce(29) based on
- linear OA(8175, 6561, F81, 38) (dual of [6561, 6486, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8159, 6561, F81, 30) (dual of [6561, 6502, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(817, 23, F81, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,81)), using
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), using
- Reed–Solomon code RS(74,81) [i]
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), 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(8182, 3496, F81, 2, 38) (dual of [(3496, 2), 6910, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8182, 3496, F81, 3, 38) (dual of [(3496, 3), 10406, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(8182, 3496, F81, 4, 38) (dual of [(3496, 4), 13902, 39]-NRT-code) | [i] | ||
| 4 | Digital (44, 82, 3496)-net over F81 | [i] | ||
| 5 | Linear OOA(8182, 3292, F81, 2, 38) (dual of [(3292, 2), 6502, 39]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8182, 2194, F81, 3, 38) (dual of [(2194, 3), 6500, 39]-NRT-code) | [i] | ||
| 7 | Linear OOA(8182, 1646, F81, 4, 38) (dual of [(1646, 4), 6502, 39]-NRT-code) | [i] | ||