Information on Result #735431
Linear OA(8137, 6727, F81, 14) (dual of [6727, 6690, 15]-code), using (u, u+v)-construction based on
- linear OA(8110, 164, F81, 7) (dual of [164, 154, 8]-code), using
- (u, u+v)-construction [i] based on
- linear OA(813, 82, F81, 3) (dual of [82, 79, 4]-code or 82-arc in PG(2,81) or 82-cap in PG(2,81)), using
- extended Reed–Solomon code RSe(79,81) [i]
- oval in PG(2, 81) [i]
- linear OA(817, 82, F81, 7) (dual of [82, 75, 8]-code or 82-arc in PG(6,81)), using
- extended Reed–Solomon code RSe(75,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82 | 812−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(813, 82, F81, 3) (dual of [82, 79, 4]-code or 82-arc in PG(2,81) or 82-cap in PG(2,81)), using
- (u, u+v)-construction [i] based on
- linear OA(8127, 6563, F81, 14) (dual of [6563, 6536, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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(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(13) ⊂ Ce(12) [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(8137, 3363, F81, 2, 14) (dual of [(3363, 2), 6689, 15]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8137, 2242, F81, 3, 14) (dual of [(2242, 3), 6689, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(8137, 961, F81, 14, 14) (dual of [(961, 14), 13417, 15]-NRT-code) | [i] | OA Folding and Stacking | |