Information on Result #684768
Linear OA(7102, 16818, F7, 24) (dual of [16818, 16716, 25]-code), using construction X applied to Ce(23) ⊂ Ce(21) based on
- linear OA(7101, 16807, F7, 24) (dual of [16807, 16706, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 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(7103, 16819, F7, 24) (dual of [16819, 16716, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(7102, 11428, F7, 2, 24) (dual of [(11428, 2), 22754, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(7102, 11428, F7, 3, 24) (dual of [(11428, 3), 34182, 25]-NRT-code) | [i] | ||
| 4 | Digital (78, 102, 11428)-net over F7 | [i] | ||
| 5 | Linear OOA(7102, 8409, F7, 2, 24) (dual of [(8409, 2), 16716, 25]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(7102, 5606, F7, 3, 24) (dual of [(5606, 3), 16716, 25]-NRT-code) | [i] | ||