Information on Result #836981
Linear OOA(5143, 39067, F5, 2, 26) (dual of [(39067, 2), 77991, 27]-NRT-code), using OOA 2-folding based on linear OA(5143, 78134, F5, 26) (dual of [78134, 77991, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5143, 78135, F5, 26) (dual of [78135, 77992, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- linear OA(5141, 78125, F5, 26) (dual of [78125, 77984, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 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]
- construction XX applied to Ce(25) ⊂ Ce(23) ⊂ Ce(22) [i] based on
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(5143, 39067, F5, 3, 26) (dual of [(39067, 3), 117058, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (117, 143, 39067)-net over F5 | [i] | ||