Information on Result #1311490
Linear OA(743, 2413, F7, 12) (dual of [2413, 2370, 13]-code), using 6 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0) based on linear OA(741, 2405, F7, 12) (dual of [2405, 2364, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(741, 2401, F7, 12) (dual of [2401, 2360, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(737, 2401, F7, 11) (dual of [2401, 2364, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(70, 4, F7, 0) (dual of [4, 4, 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
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(743, 2413, F7, 2, 12) (dual of [(2413, 2), 4783, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(743, 2413, F7, 3, 12) (dual of [(2413, 3), 7196, 13]-NRT-code) | [i] | ||
| 3 | Digital (31, 43, 2413)-net over F7 | [i] | ||