Information on Result #682970
Linear OA(582, 3131, F5, 21) (dual of [3131, 3049, 22]-code), using construction X applied to Ce(20) ⊂ Ce(18) 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(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(51, 6, F5, 1) (dual of [6, 5, 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 OA(581, 3130, F5, 20) (dual of [3130, 3049, 21]-code) | [i] | Truncation | |
| 2 | Linear OOA(582, 1879, F5, 2, 21) (dual of [(1879, 2), 3676, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(582, 1879, F5, 3, 21) (dual of [(1879, 3), 5555, 22]-NRT-code) | [i] | ||
| 4 | Digital (61, 82, 1879)-net over F5 | [i] | ||
| 5 | Linear OOA(582, 1565, F5, 2, 21) (dual of [(1565, 2), 3048, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(582, 1043, F5, 3, 21) (dual of [(1043, 3), 3047, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(582, 313, F5, 21, 21) (dual of [(313, 21), 6491, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |