Information on Result #699626
Linear OA(8166, 6596, F81, 28) (dual of [6596, 6530, 29]-code), using construction X applied to Ce(27) ⊂ Ce(15) based on
- linear OA(8155, 6561, F81, 28) (dual of [6561, 6506, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(8166, 6596, F81, 2, 28) (dual of [(6596, 2), 13126, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8166, 6596, F81, 3, 28) (dual of [(6596, 3), 19722, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(8166, 6596, F81, 4, 28) (dual of [(6596, 4), 26318, 29]-NRT-code) | [i] | ||
| 4 | Digital (38, 66, 6596)-net over F81 | [i] | ||
| 5 | Linear OOA(8166, 3298, F81, 2, 28) (dual of [(3298, 2), 6530, 29]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8166, 2198, F81, 3, 28) (dual of [(2198, 3), 6528, 29]-NRT-code) | [i] | ||
| 7 | Linear OOA(8166, 1649, F81, 4, 28) (dual of [(1649, 4), 6530, 29]-NRT-code) | [i] | ||