Information on Result #684564
Linear OA(774, 823567, F7, 12) (dual of [823567, 823493, 13]-code), using construction X applied to Ce(11) ⊂ Ce(8) based on
- linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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(73, 24, F7, 2) (dual of [24, 21, 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(774, 823567, F7, 2, 12) (dual of [(823567, 2), 1647060, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(774, 823567, F7, 3, 12) (dual of [(823567, 3), 2470627, 13]-NRT-code) | [i] | ||
| 3 | Digital (62, 74, 823567)-net over F7 | [i] | ||
| 4 | Linear OOA(774, 411783, F7, 2, 12) (dual of [(411783, 2), 823492, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(774, 274522, F7, 3, 12) (dual of [(274522, 3), 823492, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(774, 137261, F7, 12, 12) (dual of [(137261, 12), 1647058, 13]-NRT-code) | [i] | OA Folding and Stacking | |