Information on Result #731052
Linear OA(776, 235314, F7, 13) (dual of [235314, 235238, 14]-code), using trace code 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
Mode: Constructive and 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 OA(777, 235315, F7, 13) (dual of [235315, 235238, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(776, 235314, F7, 2, 13) (dual of [(235314, 2), 470552, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(776, 235314, F7, 3, 13) (dual of [(235314, 3), 705866, 14]-NRT-code) | [i] | ||
| 4 | Digital (63, 76, 235314)-net over F7 | [i] | ||
| 5 | Linear OA(777, 235316, F7, 13) (dual of [235316, 235239, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(776, 117657, F7, 2, 13) (dual of [(117657, 2), 235238, 14]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(776, 78438, F7, 3, 13) (dual of [(78438, 3), 235238, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(776, 39218, F7, 13, 13) (dual of [(39218, 13), 509758, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |