Information on Result #735439
Linear OA(8131, 6645, F81, 13) (dual of [6645, 6614, 14]-code), using (u, u+v)-construction based on
- linear OA(816, 82, F81, 6) (dual of [82, 76, 7]-code or 82-arc in PG(5,81)), using
- extended Reed–Solomon code RSe(76,81) [i]
- linear OA(8125, 6563, F81, 13) (dual of [6563, 6538, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(8125, 6561, F81, 13) (dual of [6561, 6536, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
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(8131, 6645, F81, 2, 13) (dual of [(6645, 2), 13259, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8131, 6645, F81, 3, 13) (dual of [(6645, 3), 19904, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(8131, 6645, F81, 4, 13) (dual of [(6645, 4), 26549, 14]-NRT-code) | [i] | ||
| 4 | Digital (18, 31, 6645)-net over F81 | [i] | ||
| 5 | Linear OOA(8131, 2215, F81, 3, 13) (dual of [(2215, 3), 6614, 14]-NRT-code) | [i] | OOA Folding | |