Information on Result #1324290
Linear OA(5107, 390676, F5, 15) (dual of [390676, 390569, 16]-code), using construction X with Varšamov bound based on
- linear OA(5106, 390674, F5, 15) (dual of [390674, 390568, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(8) [i] based on
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(557, 390625, F5, 9) (dual of [390625, 390568, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(59, 49, F5, 5) (dual of [49, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- construction X applied to Ce(15) ⊂ Ce(8) [i] based on
- linear OA(5106, 390675, F5, 14) (dual of [390675, 390569, 15]-code), using Gilbert–Varšamov bound and bm = 5106 > Vbs−1(k−1) = 53211 449953 440477 791391 332595 716964 327898 111532 102280 495258 008864 281049 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 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(5107, 390676, F5, 2, 15) (dual of [(390676, 2), 781245, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5107, 390676, F5, 3, 15) (dual of [(390676, 3), 1171921, 16]-NRT-code) | [i] | ||
| 3 | Digital (92, 107, 390676)-net over F5 | [i] | ||