Information on Result #731031
Linear OA(748, 4812, F7, 12) (dual of [4812, 4764, 13]-code), using trace code based on linear OA(4924, 2406, F49, 12) (dual of [2406, 2382, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4919, 2401, F49, 10) (dual of [2401, 2382, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(749, 4813, F7, 12) (dual of [4813, 4764, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(749, 4814, F7, 12) (dual of [4814, 4765, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(748, 2406, F7, 2, 12) (dual of [(2406, 2), 4764, 13]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(748, 1604, F7, 3, 12) (dual of [(1604, 3), 4764, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(748, 802, F7, 12, 12) (dual of [(802, 12), 9576, 13]-NRT-code) | [i] | OA Folding and Stacking | |