Information on Result #698044
Linear OA(4954, 5764810, F49, 14) (dual of [5764810, 5764756, 15]-code), using construction X applied to Ce(13) ⊂ Ce(11) based on
- linear OA(4953, 5764801, F49, 14) (dual of [5764801, 5764748, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 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 OOA(4954, 3214787, F49, 2, 14) (dual of [(3214787, 2), 6429520, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4954, 3214787, F49, 3, 14) (dual of [(3214787, 3), 9644307, 15]-NRT-code) | [i] | ||
| 3 | Digital (40, 54, 3214787)-net over F49 | [i] | ||
| 4 | Linear OOA(4954, 2882405, F49, 2, 14) (dual of [(2882405, 2), 5764756, 15]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4954, 1921603, F49, 3, 14) (dual of [(1921603, 3), 5764755, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(4954, 823544, F49, 14, 14) (dual of [(823544, 14), 11529562, 15]-NRT-code) | [i] | OA Folding and Stacking | |