Information on Result #684597
Linear OA(752, 823553, F7, 9) (dual of [823553, 823501, 10]-code), using construction XX applied to Ce(8) ⊂ Ce(7) ⊂ Ce(5) based on
- linear OA(750, 823543, F7, 9) (dual of [823543, 823493, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(736, 823543, F7, 6) (dual of [823543, 823507, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(70, 8, F7, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(752, 808925, F7, 2, 9) (dual of [(808925, 2), 1617798, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(752, 808925, F7, 3, 9) (dual of [(808925, 3), 2426723, 10]-NRT-code) | [i] | ||
| 3 | Digital (43, 52, 808925)-net over F7 | [i] | ||
| 4 | Linear OOA(752, 205888, F7, 9, 9) (dual of [(205888, 9), 1852940, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |