Information on Result #682530
Linear OA(5136, 78142, F5, 24) (dual of [78142, 78006, 25]-code), using construction XX applied to Ce(23) ⊂ Ce(21) ⊂ Ce(20) based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(51, 16, F5, 1) (dual of [16, 15, 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
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(5136, 44033, F5, 2, 24) (dual of [(44033, 2), 87930, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5136, 44033, F5, 3, 24) (dual of [(44033, 3), 131963, 25]-NRT-code) | [i] | ||
| 3 | Digital (112, 136, 44033)-net over F5 | [i] | ||
| 4 | Linear OOA(5136, 39071, F5, 2, 24) (dual of [(39071, 2), 78006, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5136, 26047, F5, 3, 24) (dual of [(26047, 3), 78005, 25]-NRT-code) | [i] | ||