Information on Result #682141
Linear OA(556, 1953136, F5, 8) (dual of [1953136, 1953080, 9]-code), using construction X4 applied to Ce(7) ⊂ Ce(6) based on
- linear OA(555, 1953125, F5, 8) (dual of [1953125, 1953070, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(546, 1953125, F5, 7) (dual of [1953125, 1953079, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(510, 11, F5, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,5)), using
- dual of repetition code with length 11 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-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(556, 1911553, F5, 2, 8) (dual of [(1911553, 2), 3823050, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(556, 1911553, F5, 3, 8) (dual of [(1911553, 3), 5734603, 9]-NRT-code) | [i] | ||
| 3 | Digital (48, 56, 1911553)-net over F5 | [i] | ||