Information on Result #1311467
Linear OA(729, 406, F7, 10) (dual of [406, 377, 11]-code), using 54 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 14 times 0, 1, 34 times 0) based on linear OA(725, 348, F7, 10) (dual of [348, 323, 11]-code), using
- construction XX applied to C1 = C([341,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([341,8]) [i] based on
- linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(719, 342, F7, 8) (dual of [342, 323, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 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(70, 3, F7, 0) (dual of [3, 3, 1]-code) (see above)
Mode: 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(729, 406, F7, 2, 10) (dual of [(406, 2), 783, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(729, 406, F7, 3, 10) (dual of [(406, 3), 1189, 11]-NRT-code) | [i] | ||
| 3 | Digital (19, 29, 406)-net over F7 | [i] | ||
| 4 | Linear OOA(729, 203, F7, 2, 10) (dual of [(203, 2), 377, 11]-NRT-code) | [i] | OOA Folding | |