Information on Result #730975
Linear OA(5100, 1252, F5, 27) (dual of [1252, 1152, 28]-code), using trace code based on linear OA(2550, 626, F25, 27) (dual of [626, 576, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(2550, 625, F25, 27) (dual of [625, 575, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2549, 625, F25, 26) (dual of [625, 576, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(250, 1, F25, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-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(5101, 1253, F5, 27) (dual of [1253, 1152, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5102, 1254, F5, 27) (dual of [1254, 1152, 28]-code) | [i] | ||
| 3 | Linear OA(5103, 1255, F5, 27) (dual of [1255, 1152, 28]-code) | [i] | ||
| 4 | Linear OA(599, 1251, F5, 26) (dual of [1251, 1152, 27]-code) | [i] | Truncation | |
| 5 | Linear OOA(5100, 626, F5, 2, 27) (dual of [(626, 2), 1152, 28]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5100, 417, F5, 3, 27) (dual of [(417, 3), 1151, 28]-NRT-code) | [i] | ||