Information on Result #731045
Linear OA(768, 4814, F7, 17) (dual of [4814, 4746, 18]-code), using trace code based on linear OA(4934, 2407, F49, 17) (dual of [2407, 2373, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(4933, 2402, F49, 17) (dual of [2402, 2369, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(4929, 2402, F49, 15) (dual of [2402, 2373, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(491, 5, F49, 1) (dual of [5, 4, 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(769, 4815, F7, 17) (dual of [4815, 4746, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(768, 2407, F7, 2, 17) (dual of [(2407, 2), 4746, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(768, 1604, F7, 3, 17) (dual of [(1604, 3), 4744, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(768, 601, F7, 17, 17) (dual of [(601, 17), 10149, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |