Information on Result #904737
Linear OOA(8182, 3463, F81, 2, 30) (dual of [(3463, 2), 6844, 31]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8123, 182, F81, 2, 15) (dual of [(182, 2), 341, 16]-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(8116, 100, F81, 2, 15) (dual of [(100, 2), 184, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,184P) [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(8159, 3281, F81, 2, 30) (dual of [(3281, 2), 6503, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8159, 6562, F81, 30) (dual of [6562, 6503, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8159, 6563, F81, 30) (dual of [6563, 6504, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(8159, 6561, F81, 30) (dual of [6561, 6502, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8157, 6561, F81, 29) (dual of [6561, 6504, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(29) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(8159, 6563, F81, 30) (dual of [6563, 6504, 31]-code), using
- OOA 2-folding [i] based on linear OA(8159, 6562, F81, 30) (dual of [6562, 6503, 31]-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(8182, 1731, F81, 4, 30) (dual of [(1731, 4), 6842, 31]-NRT-code) | [i] | OOA Folding | |