Information on Result #1441732
Linear OOA(777, 235316, F7, 2, 13) (dual of [(235316, 2), 470555, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(777, 235316, F7, 13) (dual of [235316, 235239, 14]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(776, 235314, F7, 13) (dual of [235314, 235238, 14]-code), using
- trace code [i] based on linear OA(4938, 117657, F49, 13) (dual of [117657, 117619, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(4937, 117650, F49, 13) (dual of [117650, 117613, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(4931, 117650, F49, 11) (dual of [117650, 117619, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 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(4938, 117657, F49, 13) (dual of [117657, 117619, 14]-code), using
- linear OA(776, 235315, F7, 12) (dual of [235315, 235239, 13]-code), using Gilbert–Varšamov bound and bm = 776 > Vbs−1(k−1) = 1 113102 965470 602409 676983 885342 570968 825662 114260 117236 545713 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(776, 235314, F7, 13) (dual of [235314, 235238, 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(777, 117658, F7, 3, 13) (dual of [(117658, 3), 352897, 14]-NRT-code) | [i] | OOA Folding | |