Information on Result #735746
Linear OA(12841, 16538, F128, 16) (dual of [16538, 16497, 17]-code), using (u, u+v)-construction based on
- linear OA(12810, 152, F128, 8) (dual of [152, 142, 9]-code), using
- construction X applied to AG(F,140P) ⊂ AG(F,142P) [i] based on
- linear OA(1289, 149, F128, 8) (dual of [149, 140, 9]-code), using algebraic-geometric code AG(F,140P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OA(1287, 149, F128, 6) (dual of [149, 142, 7]-code), using algebraic-geometric code AG(F,142P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150 (see above)
- linear OA(1281, 3, F128, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,140P) ⊂ AG(F,142P) [i] based on
- linear OA(12831, 16386, F128, 16) (dual of [16386, 16355, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [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(12841, 8269, F128, 2, 16) (dual of [(8269, 2), 16497, 17]-NRT-code) | [i] | OOA Folding | |