Information on Result #684845
Linear OA(772, 16848, F7, 15) (dual of [16848, 16776, 16]-code), using construction X applied to Ce(14) ⊂ Ce(7) based on
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(711, 41, F7, 6) (dual of [41, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(711, 48, F7, 6) (dual of [48, 37, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(711, 48, F7, 6) (dual of [48, 37, 7]-code), 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(771, 16847, F7, 14) (dual of [16847, 16776, 15]-code) | [i] | Truncation | |
| 2 | Linear OOA(772, 8424, F7, 2, 15) (dual of [(8424, 2), 16776, 16]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(772, 5616, F7, 3, 15) (dual of [(5616, 3), 16776, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(772, 2406, F7, 15, 15) (dual of [(2406, 15), 36018, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |