Information on Result #731077
Linear OA(7102, 4806, F7, 26) (dual of [4806, 4704, 27]-code), using trace code based on linear OA(4951, 2403, F49, 26) (dual of [2403, 2352, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4951, 2401, F49, 26) (dual of [2401, 2350, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4949, 2401, F49, 25) (dual of [2401, 2352, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 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 OA(7103, 4807, F7, 26) (dual of [4807, 4704, 27]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(7102, 4806, F7, 2, 26) (dual of [(4806, 2), 9510, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(7102, 4806, F7, 3, 26) (dual of [(4806, 3), 14316, 27]-NRT-code) | [i] | ||
| 4 | Digital (76, 102, 4806)-net over F7 | [i] | ||
| 5 | Linear OA(7103, 5162, F7, 26) (dual of [5162, 5059, 27]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(7102, 2403, F7, 2, 26) (dual of [(2403, 2), 4704, 27]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(7102, 1602, F7, 3, 26) (dual of [(1602, 3), 4704, 27]-NRT-code) | [i] | ||