Information on Result #1303312
Linear OA(987, 13128, F9, 22) (dual of [13128, 13041, 23]-code), using construction X with Varšamov bound based on
- linear OA(986, 13126, F9, 22) (dual of [13126, 13040, 23]-code), using
- trace code [i] based on linear OA(8143, 6563, F81, 22) (dual of [6563, 6520, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(8143, 6563, F81, 22) (dual of [6563, 6520, 23]-code), using
- linear OA(986, 13127, F9, 21) (dual of [13127, 13041, 22]-code), using Gilbert–Varšamov bound and bm = 986 > Vbs−1(k−1) = 10767 537645 293308 102918 289574 118116 887974 275199 972694 910181 925261 790755 302354 497009 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 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(987, 13128, F9, 2, 22) (dual of [(13128, 2), 26169, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(987, 13128, F9, 3, 22) (dual of [(13128, 3), 39297, 23]-NRT-code) | [i] | ||
| 3 | Digital (65, 87, 13128)-net over F9 | [i] | ||
| 4 | Linear OOA(987, 6564, F9, 2, 22) (dual of [(6564, 2), 13041, 23]-NRT-code) | [i] | OOA Folding | |