Information on Result #1449174
Linear OOA(939, 1062890, F9, 2, 7) (dual of [(1062890, 2), 2125741, 8]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(939, 1062890, F9, 7) (dual of [1062890, 1062851, 8]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(938, 1062888, F9, 7) (dual of [1062888, 1062850, 8]-code), using
- trace code [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 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(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- linear OA(938, 1062889, F9, 6) (dual of [1062889, 1062851, 7]-code), using Gilbert–Varšamov bound and bm = 938 > Vbs−1(k−1) = 370 426781 131608 262412 300373 957185 [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
- linear OA(938, 1062888, F9, 7) (dual of [1062888, 1062850, 8]-code), 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(939, 531445, F9, 3, 7) (dual of [(531445, 3), 1594296, 8]-NRT-code) | [i] | OOA Folding | |