Information on Result #683001
Linear OA(582, 3136, F5, 20) (dual of [3136, 3054, 21]-code), using construction X applied to Ce(20) ⊂ Ce(17) based on
- linear OA(581, 3125, F5, 21) (dual of [3125, 3044, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(571, 3125, F5, 18) (dual of [3125, 3054, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 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(582, 2627, F5, 2, 20) (dual of [(2627, 2), 5172, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(582, 2627, F5, 3, 20) (dual of [(2627, 3), 7799, 21]-NRT-code) | [i] | ||
| 3 | Digital (62, 82, 2627)-net over F5 | [i] | ||
| 4 | Linear OOA(582, 1568, F5, 2, 20) (dual of [(1568, 2), 3054, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(582, 1045, F5, 3, 20) (dual of [(1045, 3), 3053, 21]-NRT-code) | [i] | ||