Information on Result #684770
Linear OA(799, 16820, F7, 23) (dual of [16820, 16721, 24]-code), using construction X applied to Ce(22) ⊂ Ce(19) based on
- linear OA(796, 16807, F7, 23) (dual of [16807, 16711, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(786, 16807, F7, 20) (dual of [16807, 16721, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(73, 13, F7, 2) (dual of [13, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-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 OOA(799, 12697, F7, 2, 23) (dual of [(12697, 2), 25295, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(799, 12697, F7, 3, 23) (dual of [(12697, 3), 37992, 24]-NRT-code) | [i] | ||
| 3 | Digital (76, 99, 12697)-net over F7 | [i] | ||
| 4 | Linear OOA(799, 8410, F7, 2, 23) (dual of [(8410, 2), 16721, 24]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(799, 5606, F7, 3, 23) (dual of [(5606, 3), 16719, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(799, 1529, F7, 23, 23) (dual of [(1529, 23), 35068, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |