Information on Result #735366
Linear OA(8147, 6681, F81, 18) (dual of [6681, 6634, 19]-code), using (u, u+v)-construction based on
- linear OA(8112, 118, F81, 9) (dual of [118, 106, 10]-code), using
- construction X applied to AG(F,105P) ⊂ AG(F,107P) [i] based on
- linear OA(8111, 115, F81, 9) (dual of [115, 104, 10]-code), using algebraic-geometric code AG(F,105P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- linear OA(819, 115, F81, 7) (dual of [115, 106, 8]-code), using algebraic-geometric code AG(F,107P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116 (see above)
- linear OA(811, 3, F81, 1) (dual of [3, 2, 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 AG(F,105P) ⊂ AG(F,107P) [i] based on
- linear OA(8135, 6563, F81, 18) (dual of [6563, 6528, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8133, 6561, F81, 17) (dual of [6561, 6528, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [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(8147, 2227, F81, 3, 18) (dual of [(2227, 3), 6634, 19]-NRT-code) | [i] | OOA Folding | |