Information on Result #731515
Linear OA(9138, 13126, F9, 35) (dual of [13126, 12988, 36]-code), using trace code based on linear OA(8169, 6563, F81, 35) (dual of [6563, 6494, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(33) [i] based on
- linear OA(8169, 6561, F81, 35) (dual of [6561, 6492, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(8167, 6561, F81, 34) (dual of [6561, 6494, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 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(9139, 13127, F9, 35) (dual of [13127, 12988, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9138, 13126, F9, 2, 35) (dual of [(13126, 2), 26114, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(9138, 13126, F9, 3, 35) (dual of [(13126, 3), 39240, 36]-NRT-code) | [i] | ||
| 4 | Digital (103, 138, 13126)-net over F9 | [i] | ||
| 5 | Linear OOA(9138, 6563, F9, 2, 35) (dual of [(6563, 2), 12988, 36]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(9138, 4375, F9, 3, 35) (dual of [(4375, 3), 12987, 36]-NRT-code) | [i] | ||
| 7 | Linear OOA(9138, 772, F9, 35, 35) (dual of [(772, 35), 26882, 36]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |