Information on Result #1311714
Linear OA(765, 397, F7, 24) (dual of [397, 332, 25]-code), using 45 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 14 times 0, 1, 24 times 0) based on linear OA(761, 348, F7, 24) (dual of [348, 287, 25]-code), using
- construction XX applied to C1 = C([341,21]), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C([341,22]) [i] based on
- linear OA(758, 342, F7, 23) (dual of [342, 284, 24]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(758, 342, F7, 23) (dual of [342, 284, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(761, 342, F7, 24) (dual of [342, 281, 25]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,22}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(755, 342, F7, 22) (dual of [342, 287, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [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(765, 397, F7, 2, 24) (dual of [(397, 2), 729, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(765, 397, F7, 3, 24) (dual of [(397, 3), 1126, 25]-NRT-code) | [i] | ||
| 3 | Digital (41, 65, 397)-net over F7 | [i] | ||