Information on Result #1303391
Linear OA(9107, 1062898, F9, 18) (dual of [1062898, 1062791, 19]-code), using construction X with Varšamov bound based on
- linear OA(9106, 1062896, F9, 18) (dual of [1062896, 1062790, 19]-code), using
- trace code [i] based on linear OA(8153, 531448, F81, 18) (dual of [531448, 531395, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8146, 531441, F81, 16) (dual of [531441, 531395, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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 Ce(17) ⊂ Ce(15) [i] based on
- trace code [i] based on linear OA(8153, 531448, F81, 18) (dual of [531448, 531395, 19]-code), using
- linear OA(9106, 1062897, F9, 17) (dual of [1062897, 1062791, 18]-code), using Gilbert–Varšamov bound and bm = 9106 > Vbs−1(k−1) = 35 696393 990292 100379 527879 463135 597165 975086 726113 682063 259708 196584 106704 717657 541956 585279 897985 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(9107, 1062898, F9, 2, 18) (dual of [(1062898, 2), 2125689, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
2 | Linear OOA(9107, 1062898, F9, 3, 18) (dual of [(1062898, 3), 3188587, 19]-NRT-code) | [i] | ||
3 | Digital (89, 107, 1062898)-net over F9 | [i] | ||
4 | Linear OOA(9107, 531449, F9, 2, 18) (dual of [(531449, 2), 1062791, 19]-NRT-code) | [i] | OOA Folding |