Information on Result #684958
Linear OA(721, 2405, F7, 6) (dual of [2405, 2384, 7]-code), using construction X applied to Ce(5) ⊂ Ce(4) based on
- linear OA(721, 2401, F7, 6) (dual of [2401, 2380, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(717, 2401, F7, 5) (dual of [2401, 2384, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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: Constructive and 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(721, 2405, F7, 2, 6) (dual of [(2405, 2), 4789, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(721, 2405, F7, 3, 6) (dual of [(2405, 3), 7194, 7]-NRT-code) | [i] | ||
| 3 | Digital (15, 21, 2405)-net over F7 | [i] | ||
| 4 | Linear OA(724, 4971, F7, 6) (dual of [4971, 4947, 7]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(721, 1202, F7, 2, 6) (dual of [(1202, 2), 2383, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(721, 801, F7, 3, 6) (dual of [(801, 3), 2382, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(721, 801, F7, 6, 6) (dual of [(801, 6), 4785, 7]-NRT-code) | [i] | OA Folding and Stacking | |