Information on Result #1450045
Linear OOA(985, 13136, F9, 2, 21) (dual of [(13136, 2), 26187, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(985, 13136, F9, 21) (dual of [13136, 13051, 22]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(984, 13134, F9, 21) (dual of [13134, 13050, 22]-code), using
- trace code [i] based on linear OA(8142, 6567, F81, 21) (dual of [6567, 6525, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 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 C([0,10]) ⊂ C([0,9]) [i] based on
- trace code [i] based on linear OA(8142, 6567, F81, 21) (dual of [6567, 6525, 22]-code), using
- linear OA(984, 13135, F9, 20) (dual of [13135, 13051, 21]-code), using Gilbert–Varšamov bound and bm = 984 > Vbs−1(k−1) = 2 077686 364189 490985 883127 648593 333937 627420 666077 625744 043499 089149 751017 181489 [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(984, 13134, F9, 21) (dual of [13134, 13050, 22]-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(985, 6568, F9, 3, 21) (dual of [(6568, 3), 19619, 22]-NRT-code) | [i] | OOA Folding | |