Information on Result #1311656
Linear OA(758, 402, F7, 21) (dual of [402, 344, 22]-code), using 51 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 15 times 0, 1, 30 times 0) based on linear OA(755, 348, F7, 21) (dual of [348, 293, 22]-code), using
- construction XX applied to C1 = C([341,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([341,19]) [i] based on
- linear OA(752, 342, F7, 20) (dual of [342, 290, 21]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(752, 342, F7, 20) (dual of [342, 290, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(755, 342, F7, 21) (dual of [342, 287, 22]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(749, 342, F7, 19) (dual of [342, 293, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(758, 402, F7, 2, 21) (dual of [(402, 2), 746, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(758, 402, F7, 3, 21) (dual of [(402, 3), 1148, 22]-NRT-code) | [i] | ||
| 3 | Digital (37, 58, 402)-net over F7 | [i] | ||
| 4 | Linear OOA(758, 201, F7, 2, 21) (dual of [(201, 2), 344, 22]-NRT-code) | [i] | OOA Folding | |