Information on Result #731526
Linear OA(9142, 13126, F9, 36) (dual of [13126, 12984, 37]-code), using trace code based on linear OA(8171, 6563, F81, 36) (dual of [6563, 6492, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- linear OA(8171, 6561, F81, 36) (dual of [6561, 6490, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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(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(9143, 13127, F9, 36) (dual of [13127, 12984, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(9142, 13126, F9, 2, 36) (dual of [(13126, 2), 26110, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(9142, 13126, F9, 3, 36) (dual of [(13126, 3), 39236, 37]-NRT-code) | [i] | ||
| 4 | Digital (106, 142, 13126)-net over F9 | [i] | ||
| 5 | Linear OOA(9142, 6563, F9, 2, 36) (dual of [(6563, 2), 12984, 37]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(9142, 4375, F9, 3, 36) (dual of [(4375, 3), 12983, 37]-NRT-code) | [i] | ||