Information on Result #682997
Linear OA(5109, 3138, F5, 27) (dual of [3138, 3029, 28]-code), using construction X applied to Ce(26) ⊂ Ce(23) based on
- linear OA(5106, 3125, F5, 27) (dual of [3125, 3019, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(596, 3125, F5, 24) (dual of [3125, 3029, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(53, 13, F5, 2) (dual of [13, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-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(5109, 2644, F5, 2, 27) (dual of [(2644, 2), 5179, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5109, 2644, F5, 3, 27) (dual of [(2644, 3), 7823, 28]-NRT-code) | [i] | ||
| 3 | Digital (82, 109, 2644)-net over F5 | [i] | ||
| 4 | Linear OOA(5109, 1569, F5, 2, 27) (dual of [(1569, 2), 3029, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5109, 1046, F5, 3, 27) (dual of [(1046, 3), 3029, 28]-NRT-code) | [i] | ||