Information on Result #1311616
Linear OA(753, 401, F7, 19) (dual of [401, 348, 20]-code), using 49 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 14 times 0, 1, 28 times 0) based on linear OA(749, 348, F7, 19) (dual of [348, 299, 20]-code), using
- construction XX applied to C1 = C([341,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([341,17]) [i] based on
- linear OA(746, 342, F7, 18) (dual of [342, 296, 19]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(746, 342, F7, 18) (dual of [342, 296, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(749, 342, F7, 19) (dual of [342, 293, 20]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(753, 401, F7, 2, 19) (dual of [(401, 2), 749, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(753, 401, F7, 3, 19) (dual of [(401, 3), 1150, 20]-NRT-code) | [i] | ||
| 3 | Digital (34, 53, 401)-net over F7 | [i] | ||
| 4 | Linear OOA(753, 200, F7, 2, 19) (dual of [(200, 2), 347, 20]-NRT-code) | [i] | OOA Folding | |