Information on Result #683003
Linear OA(577, 3136, F5, 19) (dual of [3136, 3059, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- 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(566, 3125, F5, 17) (dual of [3125, 3059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(577, 2380, F5, 2, 19) (dual of [(2380, 2), 4683, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(577, 2380, F5, 3, 19) (dual of [(2380, 3), 7063, 20]-NRT-code) | [i] | ||
| 3 | Digital (58, 77, 2380)-net over F5 | [i] | ||
| 4 | Linear OOA(577, 1568, F5, 2, 19) (dual of [(1568, 2), 3059, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(577, 1045, F5, 3, 19) (dual of [(1045, 3), 3058, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(577, 348, F5, 19, 19) (dual of [(348, 19), 6535, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |