Information on Result #682191
Linear OA(576, 1953155, F5, 10) (dual of [1953155, 1953079, 11]-code), using construction X applied to Ce(10) ⊂ Ce(6) 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(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(53, 30, F5, 2) (dual of [30, 27, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), 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(576, 1953155, F5, 2, 10) (dual of [(1953155, 2), 3906234, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(576, 1953155, F5, 3, 10) (dual of [(1953155, 3), 5859389, 11]-NRT-code) | [i] | ||
| 3 | Digital (66, 76, 1953155)-net over F5 | [i] | ||
| 4 | Linear OA(577, 1953157, F5, 10) (dual of [1953157, 1953080, 11]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(576, 976577, F5, 2, 10) (dual of [(976577, 2), 1953078, 11]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(576, 651051, F5, 3, 10) (dual of [(651051, 3), 1953077, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(576, 390631, F5, 10, 10) (dual of [(390631, 10), 3906234, 11]-NRT-code) | [i] | OA Folding and Stacking | |