Information on Result #699617
Linear OA(8161, 6593, F81, 26) (dual of [6593, 6532, 27]-code), using construction X applied to Ce(25) ⊂ Ce(14) based on
- linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8129, 6561, F81, 15) (dual of [6561, 6532, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(8110, 32, F81, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,81)), using
- discarding factors / shortening the dual code based on linear OA(8110, 81, F81, 10) (dual of [81, 71, 11]-code or 81-arc in PG(9,81)), using
- Reed–Solomon code RS(71,81) [i]
- discarding factors / shortening the dual code based on linear OA(8110, 81, F81, 10) (dual of [81, 71, 11]-code or 81-arc in PG(9,81)), 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(8161, 6593, F81, 2, 26) (dual of [(6593, 2), 13125, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8161, 6593, F81, 3, 26) (dual of [(6593, 3), 19718, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(8161, 6593, F81, 4, 26) (dual of [(6593, 4), 26311, 27]-NRT-code) | [i] | ||
| 4 | Digital (35, 61, 6593)-net over F81 | [i] | ||
| 5 | Linear OOA(8161, 3296, F81, 2, 26) (dual of [(3296, 2), 6531, 27]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8161, 2197, F81, 3, 26) (dual of [(2197, 3), 6530, 27]-NRT-code) | [i] | ||
| 7 | Linear OOA(8161, 1648, F81, 4, 26) (dual of [(1648, 4), 6531, 27]-NRT-code) | [i] | ||
| 8 | Linear OOA(8161, 507, F81, 26, 26) (dual of [(507, 26), 13121, 27]-NRT-code) | [i] | OA Folding and Stacking | |