Information on Result #683000
Linear OA(589, 3138, F5, 22) (dual of [3138, 3049, 23]-code), using construction X applied to Ce(21) ⊂ Ce(18) based on
- linear OA(586, 3125, F5, 22) (dual of [3125, 3039, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(576, 3125, F5, 19) (dual of [3125, 3049, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(589, 2456, F5, 2, 22) (dual of [(2456, 2), 4823, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(589, 2456, F5, 3, 22) (dual of [(2456, 3), 7279, 23]-NRT-code) | [i] | ||
| 3 | Digital (67, 89, 2456)-net over F5 | [i] | ||
| 4 | Linear OOA(589, 1569, F5, 2, 22) (dual of [(1569, 2), 3049, 23]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(589, 1046, F5, 3, 22) (dual of [(1046, 3), 3049, 23]-NRT-code) | [i] | ||