Information on Result #1560323
Linear OOA(977, 1062900, F9, 3, 13) (dual of [(1062900, 3), 3188623, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(977, 1062900, F9, 13) (dual of [1062900, 1062823, 14]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(976, 1062898, F9, 13) (dual of [1062898, 1062822, 14]-code), using
- trace code [i] based on linear OA(8138, 531449, F81, 13) (dual of [531449, 531411, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(8137, 531442, F81, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(8131, 531442, F81, 11) (dual of [531442, 531411, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [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 C([0,6]) ⊂ C([0,5]) [i] based on
- trace code [i] based on linear OA(8138, 531449, F81, 13) (dual of [531449, 531411, 14]-code), using
- linear OA(976, 1062899, F9, 12) (dual of [1062899, 1062823, 13]-code), using Gilbert–Varšamov bound and bm = 976 > Vbs−1(k−1) = 420 939534 469201 543845 633548 125825 226705 965928 413623 471188 022427 072977 [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(976, 1062898, F9, 13) (dual of [1062898, 1062822, 14]-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(977, 531449, F9, 15, 13) (dual of [(531449, 15), 7971658, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |