Information on Result #737457
Linear OA(5134, 1953168, F5, 18) (dual of [1953168, 1953034, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(5127, 1953125, F5, 18) (dual of [1953125, 1952998, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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(57, 43, F5, 4) (dual of [43, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-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(5134, 1098152, F5, 2, 18) (dual of [(1098152, 2), 2196170, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5134, 1098152, F5, 3, 18) (dual of [(1098152, 3), 3294322, 19]-NRT-code) | [i] | ||
| 3 | Digital (116, 134, 1098152)-net over F5 | [i] | ||
| 4 | Linear OOA(5134, 976584, F5, 2, 18) (dual of [(976584, 2), 1953034, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5134, 651056, F5, 3, 18) (dual of [(651056, 3), 1953034, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(5134, 217018, F5, 18, 18) (dual of [(217018, 18), 3906190, 19]-NRT-code) | [i] | OA Folding and Stacking | |