Information on Result #735039
Linear OA(6443, 4182, F64, 17) (dual of [4182, 4139, 18]-code), using (u, u+v)-construction based on
- linear OA(649, 80, F64, 8) (dual of [80, 71, 9]-code), using
- extended algebraic-geometric code AGe(F,71P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- linear OA(6434, 4102, F64, 17) (dual of [4102, 4068, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(6429, 4097, F64, 15) (dual of [4097, 4068, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,8]) ⊂ C([0,7]) [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(6443, 2091, F64, 2, 17) (dual of [(2091, 2), 4139, 18]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(6443, 1394, F64, 3, 17) (dual of [(1394, 3), 4139, 18]-NRT-code) | [i] | ||