Information on Result #731033
Linear OA(752, 4814, F7, 13) (dual of [4814, 4762, 14]-code), using trace code based on linear OA(4926, 2407, F49, 13) (dual of [2407, 2381, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(4925, 2402, F49, 13) (dual of [2402, 2377, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(4921, 2402, F49, 11) (dual of [2402, 2381, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(753, 4815, F7, 13) (dual of [4815, 4762, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(753, 4816, F7, 13) (dual of [4816, 4763, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(752, 2407, F7, 2, 13) (dual of [(2407, 2), 4762, 14]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(752, 1604, F7, 3, 13) (dual of [(1604, 3), 4760, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(752, 802, F7, 13, 13) (dual of [(802, 13), 10374, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |