Information on Result #1449148
Linear OOA(937, 13136, F9, 2, 9) (dual of [(13136, 2), 26235, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(937, 13136, F9, 9) (dual of [13136, 13099, 10]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(936, 13134, F9, 9) (dual of [13134, 13098, 10]-code), using
- trace code [i] based on linear OA(8118, 6567, F81, 9) (dual of [6567, 6549, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- 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(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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([0,4]) ⊂ C([0,3]) [i] based on
- trace code [i] based on linear OA(8118, 6567, F81, 9) (dual of [6567, 6549, 10]-code), using
- linear OA(936, 13135, F9, 8) (dual of [13135, 13099, 9]-code), using Gilbert–Varšamov bound and bm = 936 > Vbs−1(k−1) = 28 009986 119251 897930 983990 464817 [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(936, 13134, F9, 9) (dual of [13134, 13098, 10]-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(937, 6568, F9, 3, 9) (dual of [(6568, 3), 19667, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(937, 6567, F9, 10, 9) (dual of [(6567, 10), 65633, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |