Information on Result #684836
Linear OA(762, 16838, F7, 13) (dual of [16838, 16776, 14]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
- linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(76, 31, F7, 4) (dual of [31, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-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(763, 16839, F7, 13) (dual of [16839, 16776, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(764, 16840, F7, 13) (dual of [16840, 16776, 14]-code) | [i] | ||
| 3 | Linear OA(765, 16841, F7, 13) (dual of [16841, 16776, 14]-code) | [i] | ||
| 4 | Linear OA(766, 16842, F7, 13) (dual of [16842, 16776, 14]-code) | [i] | ||
| 5 | Linear OOA(762, 8419, F7, 2, 13) (dual of [(8419, 2), 16776, 14]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(762, 5612, F7, 3, 13) (dual of [(5612, 3), 16774, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(762, 2806, F7, 13, 13) (dual of [(2806, 13), 36416, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |