Information on Result #735194
Linear OA(8174, 6683, F81, 29) (dual of [6683, 6609, 30]-code), using (u, u+v)-construction based on
- linear OA(8116, 116, F81, 14) (dual of [116, 100, 15]-code), using
- extended algebraic-geometric code AGe(F,101P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- linear OA(8158, 6567, F81, 29) (dual of [6567, 6509, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(8157, 6562, F81, 29) (dual of [6562, 6505, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(8153, 6562, F81, 27) (dual of [6562, 6509, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,14]) ⊂ C([0,13]) [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(8174, 3341, F81, 2, 29) (dual of [(3341, 2), 6608, 30]-NRT-code) | [i] | OOA Folding | |