Information on Result #904713
Linear OOA(8177, 3463, F81, 2, 28) (dual of [(3463, 2), 6849, 29]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8122, 182, F81, 2, 14) (dual of [(182, 2), 342, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(817, 82, F81, 2, 7) (dual of [(82, 2), 157, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;157,81) [i]
- linear OOA(8115, 100, F81, 2, 14) (dual of [(100, 2), 185, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,185P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- linear OOA(817, 82, F81, 2, 7) (dual of [(82, 2), 157, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8155, 3281, F81, 2, 28) (dual of [(3281, 2), 6507, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8155, 6562, F81, 28) (dual of [6562, 6507, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8155, 6563, F81, 28) (dual of [6563, 6508, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] 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(8153, 6561, F81, 27) (dual of [6561, 6508, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(27) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(8155, 6563, F81, 28) (dual of [6563, 6508, 29]-code), using
- OOA 2-folding [i] based on linear OA(8155, 6562, F81, 28) (dual of [6562, 6507, 29]-code), 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(8177, 1731, F81, 4, 28) (dual of [(1731, 4), 6847, 29]-NRT-code) | [i] | OOA Folding | |