Information on Result #699556
Linear OA(8151, 6581, F81, 23) (dual of [6581, 6530, 24]-code), using construction X applied to Ce(22) ⊂ Ce(15) based on
- linear OA(8145, 6561, F81, 23) (dual of [6561, 6516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(816, 20, F81, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,81)), using
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- Reed–Solomon code RS(75,81) [i]
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), 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(8151, 3787, F81, 2, 23) (dual of [(3787, 2), 7523, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8151, 3787, F81, 3, 23) (dual of [(3787, 3), 11310, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(8151, 3787, F81, 4, 23) (dual of [(3787, 4), 15097, 24]-NRT-code) | [i] | ||
| 4 | Digital (28, 51, 3787)-net over F81 | [i] | ||
| 5 | Linear OOA(8151, 3290, F81, 2, 23) (dual of [(3290, 2), 6529, 24]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8151, 1645, F81, 4, 23) (dual of [(1645, 4), 6529, 24]-NRT-code) | [i] | ||