Information on Result #735398
Linear OA(8160, 531565, F81, 17) (dual of [531565, 531505, 18]-code), using (u, u+v)-construction based on
- linear OA(8110, 116, F81, 8) (dual of [116, 106, 9]-code), using
- extended algebraic-geometric code AGe(F,107P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- linear OA(8150, 531449, F81, 17) (dual of [531449, 531399, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(8149, 531442, F81, 17) (dual of [531442, 531393, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(8143, 531442, F81, 15) (dual of [531442, 531399, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 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([0,8]) ⊂ 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(8160, 265782, F81, 2, 17) (dual of [(265782, 2), 531504, 18]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8160, 177188, F81, 3, 17) (dual of [(177188, 3), 531504, 18]-NRT-code) | [i] | ||