Information on Result #1559694
Linear OOA(945, 13136, F9, 3, 11) (dual of [(13136, 3), 39363, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(945, 13136, F9, 11) (dual of [13136, 13091, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(944, 13134, F9, 11) (dual of [13134, 13090, 12]-code), using
- trace code [i] based on linear OA(8122, 6567, F81, 11) (dual of [6567, 6545, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(8121, 6562, F81, 11) (dual of [6562, 6541, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(8117, 6562, F81, 9) (dual of [6562, 6545, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (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([0,5]) ⊂ C([0,4]) [i] based on
- trace code [i] based on linear OA(8122, 6567, F81, 11) (dual of [6567, 6545, 12]-code), using
- linear OA(944, 13135, F9, 10) (dual of [13135, 13091, 11]-code), using Gilbert–Varšamov bound and bm = 944 > Vbs−1(k−1) = 4290 091281 856945 993538 717786 364526 301489 [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(944, 13134, F9, 11) (dual of [13134, 13090, 12]-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(945, 6567, F9, 15, 11) (dual of [(6567, 15), 98460, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |