Information on Result #1311445
Linear OA(720, 1046, F7, 6) (dual of [1046, 1026, 7]-code), using 694 step Varšamov–Edel lengthening with (ri) = (1, 34 times 0, 1, 111 times 0, 1, 213 times 0, 1, 332 times 0) based on linear OA(716, 348, F7, 6) (dual of [348, 332, 7]-code), using
- construction XX applied to C1 = C([341,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([341,4]) [i] based on
- linear OA(713, 342, F7, 5) (dual of [342, 329, 6]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(713, 342, F7, 5) (dual of [342, 329, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(716, 342, F7, 6) (dual of [342, 326, 7]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(710, 342, F7, 4) (dual of [342, 332, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [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(720, 1046, F7, 2, 6) (dual of [(1046, 2), 2072, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(720, 1046, F7, 3, 6) (dual of [(1046, 3), 3118, 7]-NRT-code) | [i] | ||
| 3 | Digital (14, 20, 1046)-net over F7 | [i] | ||
| 4 | Linear OOA(720, 523, F7, 2, 6) (dual of [(523, 2), 1026, 7]-NRT-code) | [i] | OOA Folding | |