Information on Result #682186
Linear OA(596, 1953157, F5, 13) (dual of [1953157, 1953061, 14]-code), using construction X applied to Ce(12) ⊂ Ce(8) based on
- linear OA(591, 1953125, F5, 13) (dual of [1953125, 1953034, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(564, 1953125, F5, 9) (dual of [1953125, 1953061, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), 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(597, 1953158, F5, 13) (dual of [1953158, 1953061, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(596, 1335091, F5, 2, 13) (dual of [(1335091, 2), 2670086, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(596, 1335091, F5, 3, 13) (dual of [(1335091, 3), 4005177, 14]-NRT-code) | [i] | ||
| 4 | Digital (83, 96, 1335091)-net over F5 | [i] | ||
| 5 | Linear OOA(596, 976578, F5, 2, 13) (dual of [(976578, 2), 1953060, 14]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(596, 651052, F5, 3, 13) (dual of [(651052, 3), 1953060, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(596, 325526, F5, 13, 13) (dual of [(325526, 13), 4231742, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |