Information on Result #687216
Linear OA(8126, 4105, F8, 36) (dual of [4105, 3979, 37]-code), using construction X applied to Ce(35) ⊂ Ce(33) based on
- linear OA(8125, 4096, F8, 36) (dual of [4096, 3971, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8117, 4096, F8, 34) (dual of [4096, 3979, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-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 OOA(8126, 4021, F8, 2, 36) (dual of [(4021, 2), 7916, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8126, 4021, F8, 3, 36) (dual of [(4021, 3), 11937, 37]-NRT-code) | [i] | ||
| 3 | Digital (90, 126, 4021)-net over F8 | [i] | ||
| 4 | Linear OA(8127, 4111, F8, 36) (dual of [4111, 3984, 37]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(8126, 2052, F8, 2, 36) (dual of [(2052, 2), 3978, 37]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8126, 1368, F8, 3, 36) (dual of [(1368, 3), 3978, 37]-NRT-code) | [i] | ||