Information on Result #1311758
Linear OA(768, 358, F7, 26) (dual of [358, 290, 27]-code), using 9 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0) based on linear OA(767, 348, F7, 26) (dual of [348, 281, 27]-code), using
- construction XX applied to C1 = C([341,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([341,24]) [i] based on
- linear OA(764, 342, F7, 25) (dual of [342, 278, 26]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(764, 342, F7, 25) (dual of [342, 278, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(767, 342, F7, 26) (dual of [342, 275, 27]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(761, 342, F7, 24) (dual of [342, 281, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [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(768, 358, F7, 2, 26) (dual of [(358, 2), 648, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(768, 358, F7, 3, 26) (dual of [(358, 3), 1006, 27]-NRT-code) | [i] | ||
| 3 | Digital (42, 68, 358)-net over F7 | [i] | ||
| 4 | Linear OOA(768, 179, F7, 2, 26) (dual of [(179, 2), 290, 27]-NRT-code) | [i] | OOA Folding | |