Information on Result #684539
Linear OA(7107, 823558, F7, 18) (dual of [823558, 823451, 19]-code), using construction X applied to Ce(17) ⊂ Ce(15) based on
- linear OA(7106, 823543, F7, 18) (dual of [823543, 823437, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(71, 15, F7, 1) (dual of [15, 14, 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 OOA(7107, 449938, F7, 2, 18) (dual of [(449938, 2), 899769, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7107, 449938, F7, 3, 18) (dual of [(449938, 3), 1349707, 19]-NRT-code) | [i] | ||
| 3 | Digital (89, 107, 449938)-net over F7 | [i] | ||
| 4 | Linear OOA(7107, 411779, F7, 2, 18) (dual of [(411779, 2), 823451, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(7107, 274519, F7, 3, 18) (dual of [(274519, 3), 823450, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(7107, 91506, F7, 18, 18) (dual of [(91506, 18), 1647001, 19]-NRT-code) | [i] | OA Folding and Stacking | |