Information on Result #718382
Linear OA(9105, 123, F9, 68) (dual of [123, 18, 69]-code), using construction XX applied to C1 = C([11,69]), C2 = C([1,51]), C3 = C1 + C2 = C([11,51]), and C∩ = C1 ∩ C2 = C([1,69]) based on
- linear OA(971, 80, F9, 59) (dual of [80, 9, 60]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {11,12,…,69}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(967, 80, F9, 51) (dual of [80, 13, 52]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(976, 80, F9, 69) (dual of [80, 4, 70]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,69], and designed minimum distance d ≥ |I|+1 = 70 [i]
- linear OA(958, 80, F9, 41) (dual of [80, 22, 42]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {11,12,…,51}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(919, 28, F9, 16) (dual of [28, 9, 17]-code), using
- extended algebraic-geometric code AGe(F,11P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- extended algebraic-geometric code AGe(F,11P) [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- linear OA(910, 15, F9, 9) (dual of [15, 5, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- extended quadratic residue code Qe(20,9) [i]
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(9104, 122, F9, 67) (dual of [122, 18, 68]-code) | [i] | Truncation | |
| 2 | Linear OOA(9105, 61, F9, 2, 68) (dual of [(61, 2), 17, 69]-NRT-code) | [i] | OOA Folding | |