Information on Result #699622
Linear OA(8182, 6596, F81, 36) (dual of [6596, 6514, 37]-code), using construction X applied to Ce(35) ⊂ Ce(23) based on
- linear OA(8171, 6561, F81, 36) (dual of [6561, 6490, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(8111, 35, F81, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,81)), using
- discarding factors / shortening the dual code based on linear OA(8111, 81, F81, 11) (dual of [81, 70, 12]-code or 81-arc in PG(10,81)), using
- Reed–Solomon code RS(70,81) [i]
- discarding factors / shortening the dual code based on linear OA(8111, 81, F81, 11) (dual of [81, 70, 12]-code or 81-arc in PG(10,81)), 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, 5941, F81, 2, 36) (dual of [(5941, 2), 11800, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8182, 5941, F81, 3, 36) (dual of [(5941, 3), 17741, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(8182, 5941, F81, 4, 36) (dual of [(5941, 4), 23682, 37]-NRT-code) | [i] | ||
| 4 | Digital (46, 82, 5941)-net over F81 | [i] | ||
| 5 | Linear OOA(8182, 3298, F81, 2, 36) (dual of [(3298, 2), 6514, 37]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8182, 2198, F81, 3, 36) (dual of [(2198, 3), 6512, 37]-NRT-code) | [i] | ||
| 7 | Linear OOA(8182, 1649, F81, 4, 36) (dual of [(1649, 4), 6514, 37]-NRT-code) | [i] | ||