Information on Result #698244
Linear OA(4912, 2406, F49, 6) (dual of [2406, 2394, 7]-code), using construction X applied to Ce(5) ⊂ Ce(3) based on
- linear OA(4911, 2401, F49, 6) (dual of [2401, 2390, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(497, 2401, F49, 4) (dual of [2401, 2394, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(724, 4812, F7, 6) (dual of [4812, 4788, 7]-code) | [i] | Trace Code | |
| 2 | Linear OOA(4912, 2049, F49, 2, 6) (dual of [(2049, 2), 4086, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4912, 2049, F49, 3, 6) (dual of [(2049, 3), 6135, 7]-NRT-code) | [i] | ||
| 4 | Digital (6, 12, 2049)-net over F49 | [i] | ||
| 5 | Linear OOA(4912, 1203, F49, 2, 6) (dual of [(1203, 2), 2394, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4912, 802, F49, 3, 6) (dual of [(802, 3), 2394, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(4912, 802, F49, 6, 6) (dual of [(802, 6), 4800, 7]-NRT-code) | [i] | OA Folding and Stacking | |