Information on Result #684754
Linear OA(762, 16813, F7, 15) (dual of [16813, 16751, 16]-code), using construction X applied to Ce(14) ⊂ Ce(12) 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(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(71, 6, F7, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 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(761, 16812, F7, 14) (dual of [16812, 16751, 15]-code) | [i] | Truncation | |
| 2 | Linear OOA(762, 8716, F7, 2, 15) (dual of [(8716, 2), 17370, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(762, 8716, F7, 3, 15) (dual of [(8716, 3), 26086, 16]-NRT-code) | [i] | ||
| 4 | Digital (47, 62, 8716)-net over F7 | [i] | ||
| 5 | Linear OOA(762, 8406, F7, 2, 15) (dual of [(8406, 2), 16750, 16]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(762, 5604, F7, 3, 15) (dual of [(5604, 3), 16750, 16]-NRT-code) | [i] | ||