Information on Result #682163
Linear OA(574, 1953145, F5, 10) (dual of [1953145, 1953071, 11]-code), using construction X4 applied to Ce(10) ⊂ Ce(7) based on
- linear OA(573, 1953125, F5, 11) (dual of [1953125, 1953052, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
- dual of repetition code with length 20 [i]
- linear OA(51, 20, F5, 1) (dual of [20, 19, 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 OA(575, 1953146, F5, 10) (dual of [1953146, 1953071, 11]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(574, 1953145, F5, 2, 10) (dual of [(1953145, 2), 3906216, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(574, 1953145, F5, 3, 10) (dual of [(1953145, 3), 5859361, 11]-NRT-code) | [i] | ||
| 4 | Digital (64, 74, 1953145)-net over F5 | [i] | ||
| 5 | Linear OA(575, 1953147, F5, 10) (dual of [1953147, 1953072, 11]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(574, 390629, F5, 10, 10) (dual of [(390629, 10), 3906216, 11]-NRT-code) | [i] | OA Folding and Stacking | |