Information on Result #2277532
Linear OA(5150, 78162, F5, 26) (dual of [78162, 78012, 27]-code), using 2 times code embedding in larger space based on linear OA(5148, 78160, F5, 26) (dual of [78160, 78012, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(5141, 78125, F5, 26) (dual of [78125, 77984, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), 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(5150, 53531, F5, 2, 26) (dual of [(53531, 2), 106912, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5150, 53531, F5, 3, 26) (dual of [(53531, 3), 160443, 27]-NRT-code) | [i] | ||
| 3 | Digital (124, 150, 53531)-net over F5 | [i] | ||
| 4 | Linear OOA(5150, 26054, F5, 3, 26) (dual of [(26054, 3), 78012, 27]-NRT-code) | [i] | OOA Folding | |