Information on Result #1314451
Linear OA(2560, 769, F25, 27) (dual of [769, 709, 28]-code), using 133 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 9 times 0, 1, 19 times 0, 1, 35 times 0, 1, 59 times 0) 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: 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(2560, 769, F25, 2, 27) (dual of [(769, 2), 1478, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (33, 60, 769)-net over F25 | [i] | ||
| 3 | Linear OOA(2560, 384, F25, 2, 27) (dual of [(384, 2), 708, 28]-NRT-code) | [i] | OOA Folding | |