Information on Result #2247252
Linear OA(5113, 78132, F5, 20) (dual of [78132, 78019, 21]-code), using 1 times truncation based on linear OA(5114, 78133, F5, 21) (dual of [78133, 78019, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(51, 8, F5, 1) (dual of [8, 7, 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(5113, 42178, F5, 2, 20) (dual of [(42178, 2), 84243, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5113, 42178, F5, 3, 20) (dual of [(42178, 3), 126421, 21]-NRT-code) | [i] | ||
| 3 | Digital (93, 113, 42178)-net over F5 | [i] | ||
| 4 | Linear OOA(5113, 39066, F5, 2, 20) (dual of [(39066, 2), 78019, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5113, 26044, F5, 3, 20) (dual of [(26044, 3), 78019, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(5113, 7813, F5, 20, 20) (dual of [(7813, 20), 156147, 21]-NRT-code) | [i] | OA Folding and Stacking | |