Information on Result #1311489
Linear OA(737, 576, F7, 12) (dual of [576, 539, 13]-code), using 222 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 18 times 0, 1, 42 times 0, 1, 66 times 0, 1, 87 times 0) based on linear OA(731, 348, F7, 12) (dual of [348, 317, 13]-code), using
- construction XX applied to C1 = C([341,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([341,10]) [i] based on
- linear OA(728, 342, F7, 11) (dual of [342, 314, 12]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(728, 342, F7, 11) (dual of [342, 314, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(731, 342, F7, 12) (dual of [342, 311, 13]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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(737, 576, F7, 2, 12) (dual of [(576, 2), 1115, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(737, 576, F7, 3, 12) (dual of [(576, 3), 1691, 13]-NRT-code) | [i] | ||
| 3 | Digital (25, 37, 576)-net over F7 | [i] | ||
| 4 | Linear OOA(737, 288, F7, 2, 12) (dual of [(288, 2), 539, 13]-NRT-code) | [i] | OOA Folding | |